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Journal ArticleDOI

Chain Conditions on Semirings

01 Jan 1996-International Journal of Mathematics and Mathematical Sciences (Hindawi)-Vol. 19, Iss: 2, pp 321-326
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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Topics: Hilbert's basis theorem (60%), Chain (algebraic topology) (52%), Square matrix (51%) ...read more
Citations
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Journal ArticleDOI
TL;DR: The fuzzy setting of a left h-ideal in a hemiring is constructed, and basic properties are investigated.

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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.

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109 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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Journal ArticleDOI
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.

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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.

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24 citations


Cites background from "Chain Conditions on Semirings"

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

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Journal ArticleDOI
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.

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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.

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7 citations


Journal ArticleDOI
Sugato Gupta1, Sujit Kumar Sardar1Institutions (1)
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...

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4 citations


Journal ArticleDOI
T. K. Dutta1, Sujit Kumar Sardar1Institutions (1)
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

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3 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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References
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Journal ArticleDOI
Kenzo Iizuka1Institutions (1)

89 citations


Journal ArticleDOI

42 citations


Journal ArticleDOI
01 Jan 1972-

7 citations



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