Rings whose Elements are the Sum of a Tripotent and an Element from the Jacobson Radical
2019 ◽
Vol 62
(4)
◽
pp. 810-821
◽
Keyword(s):
AbstractThis paper is about rings $R$ for which every element is a sum of a tripotent and an element from the Jacobson radical $J(R)$. These rings are called semi-tripotent rings. Examples include Boolean rings, strongly nil-clean rings, strongly 2-nil-clean rings, and semi-boolean rings. Here, many characterizations of semi-tripotent rings are obtained. Necessary and sufficient conditions for a Morita context (respectively, for a group ring of an abelian group or a locally finite nilpotent group) to be semi-tripotent are proved.
2019 ◽
Vol 11
(2)
◽
pp. 264-270
1970 ◽
Vol 22
(2)
◽
pp. 249-254
◽
Keyword(s):
1979 ◽
Vol 20
(3)
◽
pp. 411-420
◽
1998 ◽
Vol 41
(4)
◽
pp. 481-487
◽
2016 ◽
Vol 16
(07)
◽
pp. 1750135
◽
Keyword(s):
1974 ◽
Vol 26
(1)
◽
pp. 121-129
◽
Keyword(s):
1979 ◽
Vol 28
(3)
◽
pp. 335-345
◽
2014 ◽
Vol 57
(3)
◽
pp. 609-613
◽