Almost prime submodules

2018 ◽  
Vol 13 (01) ◽  
pp. 2050019
Author(s):  
Le Phuong Thao
Keyword(s):  
Prime Ideals ◽  
Prime Submodules ◽  
Associative Rings ◽  
Almost Prime ◽  
Weakly Prime Ideals

In this paper, we introduce the notion of almost prime submodules of a given right [Formula: see text]-module and study some properties of them as a generalization of weakly prime ideals in associative rings. We will also investigate modules in which every fully invariant submodule is almost prime.

PRIMENESS IN MODULE CATEGORY

2010 ◽  
Vol 03 (01) ◽  
pp. 145-154 ◽  
Author(s):  
Nguyen Van Sanh ◽  
Nguyen Anh Vu ◽  
K. F. U. Ahmed ◽  
S. Asawasamrit ◽  
Le Phuong Thao
Keyword(s):  
Module Category ◽  
Prime Ideals ◽  
Prime Submodules ◽  
Associative Rings

We introduce the notion of prime submodules of a given right R-module and describe all properties of them as a generalization of prime ideals in associative rings.

Zariski-like topologies for lattices with applications to modules over associative rings

2019 ◽  
Vol 18 (07) ◽  
pp. 1950131
Author(s):  
Jawad Abuhlail ◽  
Hamza Hroub
Keyword(s):  
Complete Lattice ◽  
Associative Ring ◽  
Sufficient Conditions ◽  
Proper Class ◽  
Topological Properties ◽  
Left Module ◽  
Separation Axioms ◽  
Prime Submodules ◽  
Algebraic Properties ◽  
Associative Rings

We study Zariski-like topologies on a proper class [Formula: see text] of a complete lattice [Formula: see text]. We consider [Formula: see text] with the so-called classical Zariski topology [Formula: see text] and study its topological properties (e.g. the separation axioms, the connectedness, the compactness) and provide sufficient conditions for it to be spectral. We say that [Formula: see text] is [Formula: see text]-top if [Formula: see text] is a topology. We study the interplay between the algebraic properties of an [Formula: see text]-top complete lattice [Formula: see text] and the topological properties of [Formula: see text] Our results are applied to several spectra which are proper classes of [Formula: see text] where [Formula: see text] is a nonzero left module over an arbitrary associative ring [Formula: see text] (e.g. the spectra of prime, coprime, fully prime submodules) of [Formula: see text] as well as to several spectra of the dual complete lattice [Formula: see text] (e.g. the spectra of first, second and fully coprime submodules of [Formula: see text]).

ZERO-DIVISOR GRAPHS WITH RESPECT TO ALMOST PRIME IDEALS

2016 ◽  
Vol 38 (2) ◽  
pp. 201-211
Author(s):  
Malik Bataineh ◽  
Rawan AbdelAziz
Keyword(s):  
Zero Divisor ◽  
Prime Ideals ◽  
Almost Prime

scholarly journals Almost Prime Ideal in Gamma Near Ring

2018 ◽  
Vol 11 (2) ◽  
pp. 449-456
Author(s):  
Waheed Ahmad Khan ◽  
Adnan Muhammad ◽  
Abdelghani Taouti ◽  
Jameel Maki
Keyword(s):  
Prime Ideal ◽  
Primary Ideal ◽  
Prime Ideals ◽  
Almost Prime

In this manuscript we introduce the notion of almost prime ideals in 􀀀-near-rings along with few of their characterizations. We also present the interesting relations among almost prime, prime and primary ideal in 􀀀-nearrings.

On quasi-prime, weakly quasi-prime left ideals in ordered-Γ-semigroups

2010 ◽  
Vol 60 (2) ◽  
Author(s):  
Kostaq Hila
Keyword(s):  
Semigroup Forum ◽  
Prime Ideals ◽  
Ordered Semigroups ◽  
Weakly Prime Ideals

AbstractIn this paper we obtain and establish some important results in ordered Γ-semigroups extending and generalizing those for semigroups given in [PETRICH, M.: Introduction to Semigroups, Merill, Columbus, 1973] and for ordered semigroups from [KEHAYOPULU, N.: On weakly prime ideals of ordered semigroups, Math. Japon. 35 (1990), 1051–1056], [KEHAYOPULU, N.: On prime, weakly prime ideals in ordered semigroups, Semigroup Forum 44 (1992), 341–346] and [XIE, X. Y.—WU, M. F.: On quasi-prime, weakly quasi-prime left ideals in ordered semigroups, PU.M.A. 6 (1995), 105–120]. We introduce and give some characterizations about the quasi-prime and weakly quasi-prime left ideals of ordered-Γ-semigroups. We also introduce the concept of weakly m-systems in ordered Γ-semigroups and give some characterizations of the quasi-prime and weakly quasi-prime left ideals by weakly m-systems.

scholarly journals Weakly Prime Ideals in Involution po-Γ-Semigroups

2014 ◽  
Vol 54 (4) ◽  
pp. 629-638 ◽  
Author(s):  
M.Y. Abbasi ◽  
Abul Basar
Keyword(s):  
Prime Ideals ◽  
Weakly Prime Ideals

scholarly journals On a question about almost prime ideals

2016 ◽  
Vol 40 ◽  
pp. 620-623
Author(s):  
Esmaeil ROSTAMI ◽  
Reza NEKOOEI
Keyword(s):  
Prime Ideals ◽  
Almost Prime
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