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- Unit ringLearn more:✕This summary was generated using AI based on multiple online sources. To view the original source information, use the "Learn more" links.A unit ring is a ring with a multiplicative identity. It is therefore sometimes also known as a "ring with identity."mathworld.wolfram.com/UnitRing.htmlDefinition 14.3. A ring with identity is a ring R that contains an element 1R such that (14.2) 1R = 1R ; = a 8 a 2 R : Let us continue with our discussion of examples of rings. Example 1. Z, Q, R, and C are all commutative rings with identity.math.okstate.edu/people/binegar/3613/3613-l14.pdf
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The multiplicative identity is unique. For any element x in a ring R, one has x0 = 0 = 0x (zero is an absorbing element with respect to multiplication) and (–1)x = –x. If 0 = 1 in a ring R (or more generally, 0 is a unit element), then R has only one element, and is called the zero ring. See more
In mathematics, rings are algebraic structures that generalize fields: multiplication need not be commutative and See more
Products and powers
For each nonnegative integer n, given a sequence $${\displaystyle (a_{1},\dots ,a_{n})}$$ of … See moreThe concept of a module over a ring generalizes the concept of a vector space (over a field) by generalizing from multiplication of … See more
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The study of rings originated from the theory of polynomial rings and the theory of algebraic integers. … See moreWikipedia text under CC-BY-SA license Rings - Millersville University of Pennsylvania
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