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SEMICENTRAL IDEMPOTENTS IN A RING
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 Title & Authors
SEMICENTRAL IDEMPOTENTS IN A RING
Han, Juncheol; Lee, Yang; Park, Sangwon;
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 Abstract
Let R be a ring with identity 1, I(R) be the set of all nonunit idempotents in R and (R) (resp. (R)) be the set of all left (resp. right) semicentral idempotents in R. In this paper, the following are investigated: (1) (resp. ) if and only if re=ere (resp. er=ere) for all nilpotent elements if and only if (resp. ) for all if and only if fe=efe (resp. ef=efe) for all if and only if fe=efe (resp. ef=efe) for all which are isomorphic to e if and only if (resp. ) for all which are isomorphic to e where n is some positive integer; (2) For a ring R having a complete set of centrally primitive idempotents, every nonzero left (resp. right) semicentral idempotent is a finite sum of orthogonal left (resp. right) semicentral primitive idempotents, and eRe has also a complete set of primitive idempotents for any (resp. 0).
 Keywords
left (resp. right) semicentral idempotent;complete set of (centrally) primitive idempotents;
 Language
English
 Cited by
1.
Structure of Abelian rings, Frontiers of Mathematics in China, 2016  crossref(new windwow)
 References
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G. Calaugareanu, Rings with lattices of idempotents, Comm. Algebra 38 (2010), no. 3, 1050-1056. crossref(new window)

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

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

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