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Search: MSC category 13C05 ( Structure, classification theorems )

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1. CMB 2015 (vol 59 pp. 197)

Rajaee, Saeed
 Quasi-copure Submodules All rings are commutative with identity and all modules are unital. In this paper we introduce the concept of quasi-copure submodule of a multiplication $R$-module $M$ and will give some results of them. We give some properties of tensor product of finitely generated faithful multiplication modules. Keywords:multiplication module, arithmetical ring, copure submodule, radical of submodulesCategories:13A15, 13C05, 13C13, , 13C99

2. CMB 2014 (vol 57 pp. 735)

Cagliero, Leandro; Szechtman, Fernando
 On the Theorem of the Primitive Element with Applications to the Representation Theory of Associative and Lie Algebras We describe of all finite dimensional uniserial representations of a commutative associative (resp. abelian Lie) algebra over a perfect (resp. sufficiently large perfect) field. In the Lie case the size of the field depends on the answer to following question, considered and solved in this paper. Let $K/F$ be a finite separable field extension and let $x,y\in K$. When is $F[x,y]=F[\alpha x+\beta y]$ for some non-zero elements $\alpha,\beta\in F$? Keywords:uniserial module, Lie algebra, associative algebra, primitive elementCategories:17B10, 13C05, 12F10, 12E20

3. CMB 2011 (vol 55 pp. 378)

 On Modules Whose Proper Homomorphic Images Are of Smaller Cardinality Let $R$ be a commutative ring with identity, and let $M$ be a unitary module over $R$. We call $M$ H-smaller (HS for short) if and only if $M$ is infinite and $|M/N|<|M|$ for every nonzero submodule $N$ of $M$. After a brief introduction, we show that there exist nontrivial examples of HS modules of arbitrarily large cardinality over Noetherian and non-Noetherian domains. We then prove the following result: suppose $M$ is faithful over $R$, $R$ is a domain (we will show that we can restrict to this case without loss of generality), and $K$ is the quotient field of $R$. If $M$ is HS over $R$, then $R$ is HS as a module over itself, $R\subseteq M\subseteq K$, and there exists a generating set $S$ for $M$ over $R$ with $|S|<|R|$. We use this result to generalize a problem posed by Kaplansky and conclude the paper by answering an open question on JÃ³nsson modules. Keywords:Noetherian ring, residually finite ring, cardinal number, continuum hypothesis, valuation ring, JÃ³nsson moduleCategories:13A99, 13C05, 13E05, 03E50
 Artinian Local Cohomology Modules Let $R$ be a commutative Noetherian ring, $\fa$ an ideal of $R$ and $M$ a finitely generated $R$-module. Let $t$ be a non-negative integer. It is known that if the local cohomology module $\H^i_\fa(M)$ is finitely generated for all \$i Keywords:local cohomology module, Artinian module, reflexive moduleCategories:13D45, 13E10, 13C05