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- Title
On irreducible pseudo-prime spectrum of topological le-modules.
- Authors
Kumbhakar, Manas; Bhuniya, Anjan Kumar
- Abstract
An le-module M over a ring R is a complete lattice ordered additive monoid having the greatest element e together with a module like action of R. A proper submodule element n of RM is called pseudo-prime if (n : e) = {r ∈ R : re ≤ n} is a prime ideal of R. In this article we introduce the Zariski topology on the set XM of all pseudo-prime submodule elements of M and discuss interplay between topological properties of the Zariski topology on XM and algebraic properties of M. If RM is pseudo-primeful, then irreducibility of XM and Spec(R=Ann(M)) are equivalent. Also there is a one-to-one correspondence between the irreducible components of XM and the minimal pseudo-prime submodule elements in M. We show that if R is a Laskerian ring then XM has only finitely many irreducible components.
- Subjects
LATTICE theory; MONOIDS; ZARISKI surfaces; IRREDUCIBLE polynomials; SEMIGROUPS (Algebra)
- Publication
Quasigroups & Related Systems, 2018, Vol 26, Issue 2, p251
- ISSN
1561-2848
- Publication type
Article