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23. Unit (ring Theory) - Wikipedia, The Free Encyclopedia In a commutative unital ring R, the group of units U(R) acts on R via http://en.wikipedia.org/wiki/Unit_(ring_theory)

Unit (ring theory) From Wikipedia, the free encyclopedia Jump to: navigation search This article does not cite any references or sources Please help improve this article by adding citations to reliable sources . Unsourced material may be challenged and removed (December 2009) Not to be confused with Identity element Not to be confused with Unit ring In mathematics , an invertible element or a unit in a ( unital ring R refers to any element u that has an inverse element in the multiplicative monoid of R , i.e. such element v that uv vu R , where 1 R is the multiplicative identity element Unfortunately, the term unit is also used to refer to the identity element 1 R of the ring, in expressions like ring with a unit or unit ring , and also e.g. 'unit' matrix . (For this reason, some authors call 1 R "unity", and say that R is a "ring with unity" rather than "ring with a unit".) If ≠ 1 in the ring, then is not a unit. If ≠ 1 and the sum of any two non-units is not a unit, then the ring is a local ring edit Group of units Main article: Green's relations#The H and D relations The units of R form a group U R ) under multiplication, the

24. NRF: Clarity Unveils POS 'Innovation Lane' | RetailCustomerExperience.com The system also utilizes this customerfacing screen to encourage the customer to complete the tendering portion of the transaction while the associate rings the sale, saving http://www.retailcustomerexperience.com/article/3669/NRF-Clarity-unveils-POS-Inn

Get Free Membership Sign In Advertise Home ... Project Help Research Centers 3D Digital Signage Assisted Selling Bill Payment Kiosks Consumer Behavior ... Top 100 Retail Comments Amen brother! NRF: Clarity unveils POS 'Innovation Lane' Tags: CRM Customer Experience Customer Service Department Stores ... Technology Be the first! Key features include: A redesigned check-out lane that puts everything within arms' reach for cashiers, making it faster and more ergonomically efficient to handle transactions An advanced user interface featuring simpler prompts, easier to use features and a more visually-engaging screen, designed to improve efficiency and reduce training costs Advanced security features like biometric log-on that use finger print data to access information Smartphone-enabled loyalty programs which allow consumers to download loyalty cards to their phones then scan them at check out NFC (near field communication)-enabled payment processing which lets consumers "wave and go" (pass a payment card in front of reader to complete payment) Enhanced fraud prevention including image validation to reduce theft and product shrink For shoppers, this means near-instant access to information, personalized service, a more efficient shopping experience and, ultimately, a higher level of satisfaction. The Innovation Lane features a 15-inch touchscreen facing the customer that shows images of everything scanned and purchased and provides streaming audio and video of complementary items along with additional information about warranties and special offers the retailer can provide. The system also utilizes this customer-facing screen to encourage the customer to complete the tendering portion of the transaction while the associate rings the sale, saving valuable time at checkout.

25. Units And Associates Rings, Units and Associates. Units and Associates. If xy = 1, x is the left inverse of y and y is the right inverse of x. Clearly x and y are nonzero. http://www.mathreference.com/ring,unit.html

Rings, Units and Associates showHeader(2, "blring", "ring", "Rings", ""); Units and Associates If xy = 1, x is the left inverse of y and y is the right inverse of x. Clearly x and y are nonzero. If x has a left inverse w and a right inverse y they are equal. Write y = 1y = wxy = w(xy) = w1 = w. In this case x is called "invertible", or a "unit". The set of units forms a group under multiplication. If R is the ring, the group of units is denoted R . You've seen this before; Z n is the group of units mod n. Elements x and y are associates if x divides y and y divides x. show that "associate" forms an equivalence relation. Symmetry comes from the definition, and transitivity (x divides y and y divides z implies x divides z) is straightforward. Actually we need to be consistent here. Divides always means left divides, or right divides, as you prefer. Thus cx = y and ky = z, hence kcx = z. We sometimes lump an element and all its associates together. In the integers, 5 and -5 are associates. When factoring 45, we don't spend a lot of time worrying about 5 verses -5. They are essentially the same prime factor; merely associates of each other. Of course 5 does not equal -5, and sometimes the particular associate does matter. If xy =

26. Learn More About Freshwater Species | E! Science News treering techniques to the growth increments of long-lived marine and freshwater species. When we associate rings from one species with known sea surface temperatures, we can http://esciencenews.com/dictionary/freshwater.species

e! Science News About Spread the word! ... Contact Updated by artificial intelligence Sun, 31 Oct 2010, 0:30:24 EDT Learn more Tell your friends Get science news via Astronomy Space Biology Nature ... Home Learn more about freshwater species Science news articles about 'freshwater species' A Great Lakes mystery: The case of the disappearing species ... In one simple preventive measure, boats exchange their freshwater ballast for salt water ballast in the open ocean, thereby killing any freshwater species present. The study by Sepúlveda used a ... African freshwater species risk extinction WASHINGTON, March 19 (UPI) An international conservation group says many freshwater fish, crabs, dragonflies, mollusks and aquatic plants are at risk of extinction in southern Africa. Decline of freshwater species - a loss of natural capital ... decline of biodiversity represents a loss of natural capital for future generations. Freshwater ecosystems are particularly affected, as they harbour disproportionately high levels of biodiversity. ... New study reveals large scale conservation essential ... Peru are greatly impacted by ecological processes at the landscape scale." Many

27. Smithsonian Resident Associates Program - Wire-Wrapped Gemstone Rings In this workshop, students learn how to create a properly sized ring out of two materials, using just a few tools. Once you ve made one, you won t believe http://residentassociates.org/ticketing//tickets/reserve.aspx?performanceNumber=

28. Rings You’d Kill For (Or Be Killed By) – Tungsten Talk & Metal Musings: The Jul 15, 2010 Generally we associate rings with special occasions and gifts. Whether it s for weddings, anniversaries, or winning a sports championship, http://www.larsonjewelers.com/blog/jewelry/rings-with-power/

/* Layout */ @import "http://www.larsonjewelers.com/blog/wp-content/themes/larson/css/dropdown.css"; /* Theme */ @import "http://www.larsonjewelers.com/blog/wp-content/themes/larson/css/default.css"; Tungsten Rings by Tungsten Rings by Larson Jewelers: Fine and Unique Wedding Bands Home About Categories ... Login Now In: Larson Jewelers Blog Search the blog Tungsten Rings Blog Home Subscribe Facebook Twitter Recent Posts Larson Jewelers Unveils New Extra Wide Tungsten Rings Line Larson Jewelers Unveils New 4 mm Tungsten Rings for Fall Collection Flower me with love Twenty-five things a groom should have on his wedding day. Categories Celeb Weddings Community Engagement Jewelry ... Wedding Planning Pages Cast Your Vote to Ban the Wedding Ballad and Enter our Contest Search Popular Wedding Rings Tungsten Wedding Bands Black Tungsten Rings Mokume Gane Tungsten Rings Womens Tungsten Rings ... Thorsten Rings July 15th, 2010 in Jewelry Generally we associate rings with special occasions and gifts. Whether it’s for weddings, anniversaries, or winning a sports championship, we offer rings as a means of celebration. Popular Culture on the other hand has discovered ways to use rings that will punch, kick, and even kill for your attention. White Gold Rings grant superpowers You probably never thought that band around your ring finger contained magical powers capable of controlling the physical world. Well, unfortunately it doesn’t, so stop pointing the damn thing at your cat in hopes it will stop clawing at the sofa. However, this is the premise behind the DC Comic superhero: The Green Lantern. Kyle Rayner and the rest of the Green Lantern Corps are able to fly, shoot destructive beams and even become invisible with their rings. Unfortunately, the Green Lantern Corps are too honorable to battle cats.

29. Rec.arts.bodyart: Piercing FAQ 2D--Body Piercings & Their Suggested Jewelry People usually associate rings with navel piercings, but when they are made aware that the healing time is greatly reduced with virtually no chance of any irritation or scarring http://www.faqs.org/faqs/bodyart/piercing-faq/jewelry/partD/

30. Full-Text PDF - Research Article Two New Types Of Rings Defined By File Format PDF/Adobe Acrobat Quick View http://downloads.hindawi.com/journals/afs/2010/258947.pdf

31. Some Properties Of Associate And Presimplifiable Rings File Format PDF/Adobe Acrobat Quick View http://journals.tubitak.gov.tr/havuz/mat-0909-14.pdf

32. Two New Types Of Rings Defined By Using A Translational Invariant Fuzzy Subset by G Manal 2010 - Related articles http://www.hindawi.com/journals/afs/2010/258947.html

Advanced Search Hindawi Publishing Corporation Home Journals About Us About this Journal ... Table of Contents Journal Menu Abstracting and Indexing Aims and Scope Article Processing Charges Articles in Press ... How to Cite this Article Advances in Fuzzy Systems Volume 2010 (2010), Article ID 258947, 4 pages doi:10.1155/2010/258947 Research Article Two New Types of Rings Defined by Using a Translational Invariant Fuzzy Subset Manal Ghanem Department of Mathematics, Irbid National University, P.O. Box 2600, Irbid 21110, Jordan Received 4 March 2010; Revised 16 June 2010; Accepted 10 August 2010 Academic Editor: Eyke Huellermeier Abstract We use a translational invariant fuzzy subset p of a ring R to define two new types of commutative rings namely, p -presimplifiable and p -associate rings. We present some results of these rings. The interest of these results is that most of them are mirrors of corresponding results of presimplifiable and associate rings in classical ring theory. 1. Introduction Throughout this paper, all rings are assumed to be commutative with unity. If R is a ring, then

33. Two New Types Of Rings Defined By Using A Translational Invariant Fuzzy Subset by G Manal 2010 - Related articles http://www.hindawi.com/journals/afs/2010/258947.abs.html

34. Anderson , Axtell , Forman , Stickles : When Are Associates Unit Multiples? Your browser may not have a PDF reader available. Google recommends visiting our text version of this document. http://projecteuclid.org/DPubS/Repository/1.0/Disseminate?handle=euclid.rmjm/118

35. The Aggie Ring The Association of Former Students Aggie Ring Program has the honor and responsibility of protecting the integrity of the Aggie Ring. http://www.aggienetwork.com/ring/

36. RMS + PCCharge + Voiding In Point Of Sale We've experienced problems in our store where a sales associate rings in a customer charging a credit card, then the associate realizes they did not http://www.eggheadcafe.com/software/aspnet/35495460/rms--pccharge--voiding.aspx

37. Duties For Sales Associates | EHow.com Apr 14, 2010 The sales associate rings up sales on the pointof-sale cash register, handles various forms of payment and processes refunds, exchanges and http://www.ehow.com/list_6296496_duties-sales-associates.html

Family Food Health Home Money Style More Home Careers Sales Jobs ... Duties for Sales Associates More Articles Like This Sales Support Associate Job Description Hotel Sales Coordinator Duties Job Description of a Customer Service Sales Associate Job Description of a Sales Associate and Cashier Related Topics Store Sales Retail Store Sale Associate Job Description Commissions On Sales ... Assistant Duties Duties for Sales Associates By Jenny E eHow Contributor updated: April 14, 2010 I want to do this! What's This? cash image by Alexey Klementiev from Fotolia.com Sales associates handle various forms of payment for merchandise. Sales associates are responsible for attending to customers and maintaining good customer service in a retail environment. The job is physically demanding because it requires a lot of standing for extended periods, walking around the store and lifting of merchandise. Sales associates also work many varied hours that often include nights and holidays Customer Service Sales associates provide good customer service by greeting each customer, fostering a friendly atmosphere, having proper knowledge of the merchandise and offering assistance to customers. The sales associate lets the manager know if the customers have any requests. He also answers incoming calls in a professional and friendly manner and transfers calls to the proper department. Sales The sales associate rings up sales on the point-of-sale cash register, handles various forms of payment and processes refunds, exchanges and voids. Sales associates also issue gift certificates and credit slips, hold items for customers upon request and process rain checks, coupons and food stamps. They complete price changes or markdowns on seasonal or damaged items by changing the signs or tags to reflect the current price. At the end of the shift, sales associates reconcile accounts to ensure that the sales tally equals the items sold. If there are any shortages, the sales associate must determine the cause and take steps to correct the situation.

38. Platelet Septin Complexes Form Rings And Associate... [J Thromb Haemost. 2006] - by C Martínez 2006 - Cited by 14 - Related articles http://www.ncbi.nlm.nih.gov/pubmed/16706986

39. White Lantern Corps / Explore Blog Catalog Rings You €™d Kill For (Or Be Killed By) Generally we associate rings with special occasions and gifts. Whether it €™s for weddings, anniversaries, or winning a http://www.blogcatalog.com/explore/posts/white lantern corps/

40. Tubulin Rings: Curved Filaments With Limited Flexi... [J Supramol Struct. 1979] by WA Voter 1979 - Cited by 28 - Related articles http://www.ncbi.nlm.nih.gov/pubmed/513771

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