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1. CMB 2013 (vol 57 pp. 159)
Strongly $0$-dimensional Modules In a multiplication module, prime submodules have the property, if a prime
submodule contains a finite intersection of submodules then one of the
submodules is contained in the prime submodule. In this paper, we generalize
this property to infinite intersection of submodules and call such prime
submodules strongly prime submodule. A multiplication module in which every
prime submodule is strongly prime will be called strongly 0-dimensional
module. It is also an extension of strongly 0-dimensional rings. After
this we investigate properties of strongly 0-dimensional modules and give
relations of von Neumann regular modules, Q-modules and strongly
0-dimensional modules.
Keywords:strongly 0-dimensional rings, Q-module, Von Neumann regular module Categories:13C99, 16D10 |
2. CMB 2009 (vol 52 pp. 267)
Extensions of Rings Having McCoy Condition Let $R$ be an associative ring with unity.
Then $R$ is said to be a {\it right McCoy ring} when the equation
$f(x)g(x)=0$ (over $R[x]$), where $0\neq f(x),g(x) \in R[x]$,
implies that there exists a nonzero element $c\in R$ such that
$f(x)c=0$. In this paper, we characterize some basic ring
extensions of right McCoy rings and we prove that if $R$ is a
right McCoy ring, then $R[x]/(x^n)$ is
a right McCoy ring for any positive integer $n\geq 2$ .
Keywords:right McCoy ring, Armendariz ring, reduced ring, reversible ring, semicommutative ring Categories:16D10, 16D80, 16R50 |
3. CMB 1997 (vol 40 pp. 221)
On semiregular rings whose finitely generated modules embed in free modules We consider rings as in the title and find the precise obstacle for them not
to be Quasi-Frobenius, thus shedding new light on an old open question in
Ring Theory. We also find several partial affirmative answers for that
question.
Categories:16D10, 16L60, 16N20 |