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A class of rings with the 2-sum property.
- Source :
- Applicable Algebra in Engineering, Communication & Computing; Jun2021, Vol. 32 Issue 3, p399-408, 10p
- Publication Year :
- 2021
-
Abstract
- Recall that a ring satisfies the 2-sum property if each of its elements is a sum of two units. Here a ring R is said to satisfy the binary 2-sum property if, for any a, b in R, there exists a unit u of R such that both a - u and b - u are units. A well-known result, due to Goldsmith, Pabst and Scot, states that a semilocal ring satisfies the 2-sum property iff it has no image isomorphic to Z 2 . It is proved here that a semilocal ring satisfies the binary 2-sum property iff it has no image isomorphic to Z 2 or Z 3 or M 2 (Z 2) . [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 09381279
- Volume :
- 32
- Issue :
- 3
- Database :
- Complementary Index
- Journal :
- Applicable Algebra in Engineering, Communication & Computing
- Publication Type :
- Academic Journal
- Accession number :
- 150472747
- Full Text :
- https://doi.org/10.1007/s00200-021-00490-y