Prime and radical submodules of modules over commutative rings

ME Moore, SJ Smith - Communications in Algebra, 2002 - Taylor & Francis
In this paper, unless otherwise stated, all rings are commutative with identity and all modules
are unital. We give sufficient conditions to ensure that a submodule has a module-reduced …

Classical Zariski topology of modules and spectral spaces I

M Behboodi, MR Haddadi - International Electronic Journal of …, 2008 - dergipark.org.tr
Let R be a ring, M be a left R-module and Spec (RM) be the collection of all prime
submodules of M. In this paper and its sequel, we introduce and study a generalization of …

A generalization of the Zariski topology of arbitrary rings for modules

M Behboodi, SH Shojaee - East West Math, 2009 - enfo.ntt.edu.vn
Let M be a left R-module. The set of all prime submodules of M is called the spectrum of M
and denoted by Spec (RM), and that of all prime ideals of R is denoted by Spec (R). For …

[PDF][PDF] ON (n-1; n)-phi-m-PRIME AND (n-1; n)-WEAKLY PRIME SUBMODULES

M Ebrahimpour, F Mirzaee - Journal of Algebraic Systems, 2018 - jas.shahroodut.ac.ir
Let m; n≥ 2 be two positive integers, R a commutative ring with identity and M a unitary R-
module. A proper submodule P of M is an (n􀀀 1; n)-Φm-prime ((n􀀀 1; n)-weakly prime) …

[PDF][PDF] ON RADICALS OF PRIMARY SUBMODULES SATISFYING THE PRIMEFUL PROPERTY

F RASHEDI, MH FAZAELI, N SARVGHAD - 2013 - sid.ir
Archive of SID www.SID.ir Page 1 The Extended Abstracts of Posters of The 44th Annual Iranian
Mathematics Conference 27-30 August 2013, Ferdowsi University of Mashhad, Iran. ON …

[图书][B] Prime and radical submodules of modules over commutative rings

SJ Smith - 2001 - search.proquest.com
Prime and radical ideals have been studied extensively in commutative ring theory. This
paper attempts to extend some of the properties and uses of prime and radical ideals to …