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According to Jacobson \cite{Jacobson}, a right ideal is bounded if it contains a non-zero ideal, and Faith \cite{Faith2} called a ring strongly right bounded if every non-zero right ideal is bounded. From \cite{Hwang}, 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 \cite{Nielsen}. It is shown that for a u.p.-monoid $M$ and $\sigma: M \rightarrow {\rm End}(R)$ a compatible monoid homomorphism, if $R$ is reversible, then the skew monoid ring $R\ast M$ is strongly right $AB$. If $R$ is a strongly right $AB$ ring, $M$ is a u.p.-monoid and $\sigma: M \rightarrow {\rm End}(R)$ is a weakly rigid monoid homomorphism, then the skew monoid ring $R\ast M$ has right Property $(A)$.
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참고문헌 (50)
참고문헌 신청
D. D. Anderson / 1998 / Armendariz rings and Gaussian rings / Comm. Algebra 26(7):2265~2272
E. P. Armendariz / 1974 / A note on extensions of Baer and p.p.-rings / J. Austral. Math. Soc 18:470~473
F. Azarpanah / 2000 / On ideals consisting entirely of zero divisors / Comm. Algebra 28(2):1061~1073
J. A. Beachy / 1975 / Rings whose faithful left ideals are cofaithful / Pacific J. Math 58(1):1~13
H. E. Bell / 1970 / Near-rings in which each element is a power of itself / Bull. Austral. Math. Soc 2:363~368
E. P. Armendariz / 1974 / A note on extensions of Baer and p.p.-rings / J. Austral. Math. Soc 18:470~473
F. Azarpanah / 2000 / On ideals consisting entirely of zero divisors / Comm. Algebra 28(2):1061~1073
J. A. Beachy / 1975 / Rings whose faithful left ideals are cofaithful / Pacific J. Math 58(1):1~13
H. E. Bell / 1970 / Near-rings in which each element is a power of itself / Bull. Austral. Math. Soc 2:363~368
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