Filomat 2018 Volume 32, Issue 13, Pages: 4461-4472
https://doi.org/10.2298/FIL1813461H
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Some structure spaces of generalized semirings
Hila Kostaq
Kar Sukhendu
Kuka Shkëlqim
Naka Krisanthi
In this paper, we study some structure spaces of (m,n)-semiring (S,f,1),
introducing the classes of n-ary prime k-ideals, n-ary prime full k-ideals,
n-ary prime ideals, maximal ideals and strongly irreducible ideals.
Considering their collections, respectively, of an (m,n)-semiring (S,f,
1), we construct the respective topologies on them by means of closure
operator defined in terms of intersection and inclusion relation among these
ideals of the (m,n)-semiring (S,f,1). The obtained topological spaces are
called the structure spaces of (m,n)-semiring (S,f,1). We mainly study
several principal topological axioms and properties of those structure
spaces of (m,n)-semiring such as separation axioms, compactness and
connectedness etc.
Keywords: (m,n)-semiring, n-ary prime k-ideal, n-ary prime full k-ideal, maximal ideal, strongly irreducible ideal, structure spaces