Autor:	Ashrafi, Nahid
Další autoři:	Sheibani, Marjan Chen, Huanyin, 1963-
Jazyk:	angličtina
Předmět:	matematika mathematics články journal articles weakly nil clean ring idempotent element nilpotent element nil clean ring
Druh dokumentu:	Non-fiction
ISSN:	0011-4642
Abstrakt:	Abstract: A ring R is (weakly) nil clean provided that every element in R is the sum of a (weak) idempotent and a nilpotent. We characterize nil and weakly nil matrix rings over abelian rings. Let R be abelian, and let n 2 N. We prove that Mn(R) is nil clean if and only if R/J(R) is Boolean and Mn(J(R)) is nil. Furthermore, we prove that R is weakly nil clean if and only if R is periodic; R/J(R) is Z3, B or Z3 B where B is a Boolean ring, and that Mn(R) is weakly nil clean if and only if Mn(R) is nil clean for all n > 2.
Databáze:	Katalog Knihovny AV ČR
Externí odkaz:	Plný text Full text from SpringerLink