JP Journal of Algebra, Number Theory and Applications
Volume 24, Issue 1, Pages 115 - 124
(February 2012)
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M-STRONGLY IRREDUCIBLE IDEALS
A. Abbasi, D. Hassanzadeh-Lelekaami and M. Mirabnejad-Fashkhami
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Abstract: Let M be a module over a commutative ring R. In this paper, we introduce the notion of M-strongly irreducible ideals of R. We use this type of ideals to define a topology relative to ring R and R-module M. We investigate the relationship between algebraic properties of M and R and also, we study topological properties of the topology on the set of all M-strongly irreducible ideals of R. Moreover, modules whose topologies are irreducible or Noetherian are studied. |
Keywords and phrases: strongly irreducible submodule, M-strongly irreducible ideal, Zariski topology, spectral space. |
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