GDL

Journal from gdlhub / 2017-08-21 14:40:17
Oleh : S. Kar, S. Purkait, B. Davvaz, Fuzzy Information and Engineering
Dibuat : 2015-12-21, dengan 1 file

Keyword : Semiringk-idealFuzzy primary idealsFuzzy k-primary idealFuzzy k-primary decomposition
Url : http://www.sciencedirect.com/science/article/pii/S1616865815000813
Sumber pengambilan dokumen : web

In this paper, we establish that the Lasker–Noether theorem for a commutative ring may be generalized for a commutative semiring. We produce an example of an ideal in a Noetherian semiring which cannot be expressed as finite intersection of primary ideals of that semiring. But we manifest that if we consider an arbitrary k-ideal of a commutative Noetherian semiring, then it can be decomposed as finite intersection of primary k-ideals. Focus mainly on the fuzzy version of the above result, we are able to prove that in a commutative Noetherian semiring, every fuzzy k-ideal can be decomposed uniquely as finite intersection of fuzzy k-primary ideals of that semiring.

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