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A ring is nil-clean if every element is a sum of a nilpotent and an idempotent, and a ring is involution-clean if every element is a sum of an involution and an idempotent. In this paper, a description of nil-clean rings of nilpotency index at most $2$ is obtained, and is applied to improve a known result on involution-clean rings.
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참고문헌 (6)
참고문헌 신청
E. P. Armendariz / 1982 / On semiprime rings of bounded index / Proc. Amer. Math. Soc. 85(2):146~148
K. I. Beidar / 1997 / On rings with zero total / Beitrage Algebra Geom. 38(2):233~239
Peter V. Danchev / 2017 / Invo-clean unital rings / 대한수학회논문집 32(1):19~27
A. J. Diesl / 2013 / Nil clean rings / J. Algebra 383:197~211
T. Kosan / 2014 / When is every matrix over a division ring a sum of an idempotent and a nilpotent? / Linear Algebra Appl. 450:7~12
K. I. Beidar / 1997 / On rings with zero total / Beitrage Algebra Geom. 38(2):233~239
Peter V. Danchev / 2017 / Invo-clean unital rings / 대한수학회논문집 32(1):19~27
A. J. Diesl / 2013 / Nil clean rings / J. Algebra 383:197~211
T. Kosan / 2014 / When is every matrix over a division ring a sum of an idempotent and a nilpotent? / Linear Algebra Appl. 450:7~12
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