# Chain Conditions on Semirings

01 Jan 1996-International Journal of Mathematics and Mathematical Sciences (Hindawi)-Vol. 19, Iss: 2, pp 321-326

TL;DR: In this article, the class of semirings S for which the semiirings of square matrices Mn(S) over S are (left) k-artinian is characterized.

Abstract: In this paper we characterize the class of semirings S for which the semirings of square matrices Mn(S) over S are (left) k-artinian. Also an analogue of the Hilbert basis theorem for semirings is obtained.

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TL;DR: The fuzzy setting of a left h-ideal in a hemiring is constructed, and basic properties are investigated.

Abstract: The fuzzy setting of a left h-ideal in a hemiring is constructed, and basic properties are investigated. Using a collection of left h-ideals of a hemiring S, fuzzy left h-ideals of S are established. The notion of a finite valued fuzzy left h-ideal is introduced, and its characterization is given. Fuzzy relations on a hemiring S are discussed.

111 citations

### Cites background from "Chain Conditions on Semirings"

...A semiring S is said to be left h-Noetherian (see [17]) if it satisfies the ascending chain condition on left h-ideals of S....

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TL;DR: The notion of T-fuzzy left h-ideals in a hemiring is introduced and basic properties are investigated, and the notion of a finite-valued T-magnifying-h-ideal is introduced, and its characterization is given.

Abstract: The notion of T-fuzzy left h-ideals in a hemiring is introduced and basic properties are investigated. Using a collection of left h-ideals of a hemiring S, T-fuzzy left h-ideals of S are established. The notion of a finite-valued T-fuzzy left h-ideal is introduced, and its characterization is given. T-fuzzy relations on a hemiring S are discussed.

24 citations

### Cites background from "Chain Conditions on Semirings"

...T-fuzzy relations on a hemiring S are discussed....

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TL;DR: The notion of fuzzy ideals in nearrings with respect to a t-norm T is introduced and some properties of T-fuzzy ideals of the quotient nearrings are considered.

Abstract: We introduce the notion of fuzzy ideals in nearrings with respect to a t-norm T and investigate some of their properties. Using T-fuzzy ideals, characterizations of Artinian and Noetherian nearrings are established. Some properties of T-fuzzy ideals of the quotient nearrings are also considered.

11 citations

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TL;DR: In this paper, the authors studied Noetherian Γ-semirings and obtained Cohen's theorem for weak primary decomposition for a special class of Γ semirings.

Abstract: In this paper we study Noetherian Γ-semirings and obtain Cohen’s theorem for a special class of Γ-semirings Weak primary decomposition theorem for a particular type of Γ-semirings is also obtained

4 citations

### Cites methods from "Chain Conditions on Semirings"

...Now we have the following characterization of right h-(k-)Noetherian G-semiring which is analogous to that of semiring theory ([ 9 ]):...

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TL;DR: In this paper, the counterparts of most of the results on Morita invariants of semirings for semimodules are investigated and the lattice isomorphisms between the s...

Abstract: The purpose of this paper is to investigate the counterparts of most of our results on Morita invariants of semirings for semimodules. Among others, we obtain the lattice isomorphisms between the s...

4 citations

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