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In mathematics, a von Neumann regular ring is a ring R such that for every element a in R there exists an x in R with a = axa. One may think of x as a "weak inverse" of the element a; in general x is not uniquely determined by a. Von Neumann regular rings are also called absolutely flat rings, because these rings are characterized by the fact that every left R-module is flat.
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In mathematics, a noncommutative ring is a ring whose multiplication is not commutative; that is, there exist a and b in the ring such that ab and ba are different. Equivalently, a noncommutative ring is a ring that is not a commutative ring.
References
- ↑ Jacobson 1989, p 418.
- Jacobson, Nathan (1989), Basic algebra. II (2 ed.), New York: W. H. Freeman and Company, pp. xviii+686, ISBN 0-7167-1933-9, MR 1009787
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