ON ANNIHILATIONS OF IDEALS IN SKEW MONOID RINGS

Title & Authors
ON ANNIHILATIONS OF IDEALS IN SKEW MONOID RINGS

Abstract
According to Jacobson [31], a right ideal is bounded if it contains a non-zero ideal, and Faith [15] called a ring strongly right bounded if every non-zero right ideal is bounded. From [30], a ring is strongly right AB if every non-zero right annihilator is bounded. In this paper, we introduce and investigate a particular class of McCoy rings which satisfy Property (A) and the conditions asked by Nielsen [42]. It is shown that for a u.p.-monoid M and $\small{{\sigma}:M{\rightarrow}End(R)}$ a compatible monoid homomorphism, if R is reversible, then the skew monoid ring R * M is strongly right AB. If R is a strongly right AB ring, M is a u.p.-monoid and $\small{{\sigma}:M{\rightarrow}End(R)}$ is a weakly rigid monoid homomorphism, then the skew monoid ring R * M has right Property (A).
Keywords
skew monoid ring;McCoy ring;strongly right AB ring;nil-reversible ring;CN ring;rings with Property (A);zip ring;
Language
English
Cited by
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