SEMICENTRAL IDEMPOTENTS IN A RING

Title & Authors
SEMICENTRAL IDEMPOTENTS IN A RING
Han, Juncheol; Lee, Yang; Park, Sangwon;

Abstract
Let R be a ring with identity 1, I(R) be the set of all nonunit idempotents in R and $\small{S_{\ell}}$(R) (resp. $\small{S_r}$(R)) be the set of all left (resp. right) semicentral idempotents in R. In this paper, the following are investigated: (1) $\small{e{\in}S_{\ell}(R)}$ (resp. $\small{e{\in}S_r(R)}$) if and only if re
Keywords
left (resp. right) semicentral idempotent;complete set of (centrally) primitive idempotents;
Language
English
Cited by
1.
A note on semicentral idempotents, Communications in Algebra, 2017, 45, 6, 2735
2.
Structure of Abelian rings, Frontiers of Mathematics in China, 2017, 12, 1, 117
References
1.
G. F. Birkenmeier, H. E. Heatherly, J. Y. Kim, and J. K. Park, Triangular matrix repre-sentations, J. Algebra 230 (2000), no. 2, 558-595.

2.
G. Calaugareanu, Rings with lattices of idempotents, Comm. Algebra 38 (2010), no. 3, 1050-1056.

3.
H. K. Grover, D. Khurana, and S. Singh, Rings with multiplicative sets of primitive idempotents, Comm. Algebra 37 (2009), no. 8, 2583-2590.

4.
J. Han and S. Park, Additive set of idempotents in rings, Comm. Algebra 40 (2012), no. 9, 3551-3557.

5.
T. Y. Lam, A First Course in Noncommutative Rings, Springer-Verlag, New York, Inc., 1991.