Ideal Theory in Commutative Semirings
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EBRAHIMIATANI, Reza, ATANI, Shahabaddin Ebrahimi. Ideal Theory in Commutative Semirings. In: Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, 2008, nr. 2(57), pp. 14-23. ISSN 1024-7696.
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Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica
Numărul 2(57) / 2008 / ISSN 1024-7696 /ISSNe 2587-4322

Ideal Theory in Commutative Semirings

Pag. 14-23

EbrahimiAtani Reza, Atani Shahabaddin Ebrahimi
 
Institute of Mathematics and Computer Science ASM
 
Disponibil în IBN: 6 decembrie 2013


Rezumat

In this paper, we analyze some results on ideal theory of commutative semirings with non-zero identity analogues to commutative rings with non-zero identity. Here we will make an intensive examination of the notions of Noetherian semirings, Artinian semirings, local semirings and strongly irreducible ideals in commutative semirings. It is shown that this notion inherits most of essential properties of strongly irreducible ideals of a commutative rings with non-zero identity. Also, the relationship among the families of primary ideals, irreducible ideals and strongly irreducible ideals of a semiring R is considered.

Cuvinte-cheie
Semiring, primary,

Local,

Strongly irreducible