Frontiers of Mathematics in China >
π-Armendariz rings relative to a monoid
Received date: 24 Sep 2015
Accepted date: 19 Apr 2016
Published date: 30 Aug 2016
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Let Mbe a monoid. A ring Ris called M-π-Armendariz if whenever α = a1g1+ a2g2+ · · · + angn, β = b1h1+ b2h2+ · · · + bmhm ∈ R[M] satisfy αβ ∈ nil(R[M]), then aibj ∈ nil(R) for all i, j. A ring R is called weakly 2-primal if the set of nilpotent elements in R coincides with its Levitzki radical. In this paper, we consider some extensions of M-π-Armendariz rings and further investigate their properties under the condition that R is weakly 2-primal. We prove that if R is an M-π-Armendariz ring then nil(R[M]) = nil(R)[M]. Moreover, we study the relationship between the weak zip-property (resp., weak APP-property, nilpotent p.p.-property, weak associated prime property) of a ring R and that of the monoid ring R[M] in case R is M-π-Armendariz.
Yao WANG , Meimei JIANG , Yanli REN . π-Armendariz rings relative to a monoid[J]. Frontiers of Mathematics in China, 2016 , 11(4) : 1017 -1036 . DOI: 10.1007/s11464-016-0561-8
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