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- Title
ON THE CLASSICAL PRIME SPECTRUM OF LATTICE MODULES.
- Authors
Girase, Pradip; Borkar, Vandeo; Phadatare, Narayan
- Abstract
Let M be a lattice module over a C-lattice L. A proper element P of M is said to be classical prime if for a, b ∈ L and X ∈ M, abX ≤ P implies that aX ≤ P or bX ≤ P. The set of all classical prime elements of M, Speccp(M) is called as classical prime spectrum. In this article, we introduce and study a topology on Speccp(M), called as Zariski-like topology of M. We investigate this topological space from the point of view of spectral spaces. We show that if M has ascending chain condition on classical prime radical elements, then Speccp(M) with the Zariski-like topology is a spectral space.
- Subjects
LATTICE theory; ZARISKI surfaces; RING theory; MODULES (Algebra); MATHEMATICS theorems
- Publication
International Electronic Journal of Algebra, 2019, Vol 25, p186
- ISSN
1306-6048
- Publication type
Article
- DOI
10.24330/ieja.504147