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Search: MSC category 13A99 ( None of the above, but in this section )

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1. CMB 2013 (vol 57 pp. 413)

Samei, Karim
 On the Comaximal Graph of a Commutative Ring Let \$R\$ be a commutative ring with \$1\$. In [P. K. Sharma, S. M. Bhatwadekar, A note on graphical representation of rings, J. Algebra 176(1995) 124-127], Sharma and Bhatwadekar defined a graph on \$R\$, \$\Gamma(R)\$, with vertices as elements of \$R\$, where two distinct vertices \$a\$ and \$b\$ are adjacent if and only if \$Ra + Rb = R\$. In this paper, we consider a subgraph \$\Gamma_2(R)\$ of \$\Gamma(R)\$ which consists of non-unit elements. We investigate the behavior of \$\Gamma_2(R)\$ and \$\Gamma_2(R) \setminus \operatorname{J}(R)\$, where \$\operatorname{J}(R)\$ is the Jacobson radical of \$R\$. We associate the ring properties of \$R\$, the graph properties of \$\Gamma_2(R)\$ and the topological properties of \$\operatorname{Max}(R)\$. Diameter, girth, cycles and dominating sets are investigated and the algebraic and the topological characterizations are given for graphical properties of these graphs. Keywords:comaximal, Diameter, girth, cycles, dominating setCategory:13A99

2. CMB 2012 (vol 56 pp. 683)

Nikseresht, A.; Azizi, A.
 Envelope Dimension of Modules and the Simplified Radical Formula We introduce and investigate the notion of envelope dimension of commutative rings and modules over them. In particular, we show that the envelope dimension of a ring, \$R\$, is equal to that of the \$R\$-module \$R^{(\mathbb{N})}\$. Also we prove that the Krull dimension of a ring is no more than its envelope dimension and characterize Noetherian rings for which these two dimensions are equal. Moreover we generalize and study the concept of simplified radical formula for modules, which we defined in an earlier paper. Keywords:envelope dimension, simplified radical formula, prime submoduleCategories:13A99, 13C99, 13C13, 13E05

3. CMB 2011 (vol 55 pp. 378)