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169
COMMUTATIVE SEMIRINGS AND THEIR LATTICES OF IDEALS
"... ABSTRACT. We investigate commutative semirings and their lattices of ideals. A commutative semiring (R, +,.) is an additive abelian monoid (R, +) with identity 0 and (R,.) is a commutative monoid with identity 1 satisfying 0a = 0 and a(b + c) = ab + ac for all a,b,c E R. We investigate semirings R ..."
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ABSTRACT. We investigate commutative semirings and their lattices of ideals. A commutative semiring (R, +,.) is an additive abelian monoid (R, +) with identity 0 and (R,.) is a commutative monoid with identity 1 satisfying 0a = 0 and a(b + c) = ab + ac for all a,b,c E R. We investigate semirings R
THE TOTAL GRAPH OF A COMMUTATIVE SEMIRING
"... We introduce and investigate the total graph of a commutative semiring with nonzero identity. The main purpose of this paper is to extend the definition and some results given in [2] to a more general semiring case. 1 ..."
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We introduce and investigate the total graph of a commutative semiring with nonzero identity. The main purpose of this paper is to extend the definition and some results given in [2] to a more general semiring case. 1
ON ANTICOMMUTATIVE SEMIRINGS
, 1988
"... ABSTRACT. An anticommutative semiring is completely characterized by the types of multiplications that are permitted. It is shown that a semiring is anticommutative if and only if it is a product of two semirings R and R2 such that R is left multiplicative and R2 is right multiplicative. ..."
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ABSTRACT. An anticommutative semiring is completely characterized by the types of multiplications that are permitted. It is shown that a semiring is anticommutative if and only if it is a product of two semirings R and R2 such that R is left multiplicative and R2 is right multiplicative.
IDEMPOTENT SUBREDUCTS OF SEMIMODULES OVER COMMUTATIVE SEMIRINGS
"... Abstract. A short proof of the characterization of idempotent subreducts of semimodules over commutative semirings is presented. It says that an idempotent algebra embeds into a semimodule over a commutative semiring, if and only if it belongs to the variety of Szendrei modes. 1. ..."
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Abstract. A short proof of the characterization of idempotent subreducts of semimodules over commutative semirings is presented. It says that an idempotent algebra embeds into a semimodule over a commutative semiring, if and only if it belongs to the variety of Szendrei modes. 1.
On primal and weakly primal ideals over commutative semirings
, 2008
"... Abstract. Since the theory of ideals plays an important role in the theory of semirings, in this paper we will make an intensive study of the notions of primal and weakly primal ideals in commutative semirings with an identity 1. It is shown that these notions inherit most of the essential propertie ..."
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Cited by 2 (2 self)
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Abstract. Since the theory of ideals plays an important role in the theory of semirings, in this paper we will make an intensive study of the notions of primal and weakly primal ideals in commutative semirings with an identity 1. It is shown that these notions inherit most of the essential
PSpaces and the Prime Spectrum of Commutative Semirings
"... By a semiring we understand a commutative semiring with nonzero identity. The notions of ωabsolutely (semiprime) irreducible ideals in a semiring R are introduced and we prove that the prime spectrum Spec(R) of R is a Pspace if and only if every prime ideal of R is ωabsolutely semiprimeirreduci ..."
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By a semiring we understand a commutative semiring with nonzero identity. The notions of ωabsolutely (semiprime) irreducible ideals in a semiring R are introduced and we prove that the prime spectrum Spec(R) of R is a Pspace if and only if every prime ideal of R is ωabsolutely semiprime
Inversion of matrices over a commutative semiring
 J. Algebra
, 1984
"... It is a wellknown consequence of the elementary theory of vector spaces that if A and B are nbyn matrices over a field (or even a skew field) such that AB = 1, then BA = 1. This result remains true for matrices over a commutative ring, however, it is not, in general, true for matrices over noncom ..."
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Cited by 10 (0 self)
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noncommutatives rings. In this paper we show that if A and B are nbyn matrices over a commutative semiring, then the equation AB = 1 implies BA = 1. We give two proofs: one algebraic in nature, the other more combinatorial. Both proofs use a generalization of the familiar product law for determinants over a
Convergence of Newton’s Method over Commutative Semirings ⋆
"... Abstract. We give a lower bound on the speed at which Newton’s method (as defined in [5, 6]) converges over arbitrary ωcontinuous commutative semirings. From this result, we deduce that Newton’s method converges within a finite number of iterations over any semiring which is “collapsed at some k ∈ ..."
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Cited by 4 (3 self)
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Abstract. We give a lower bound on the speed at which Newton’s method (as defined in [5, 6]) converges over arbitrary ωcontinuous commutative semirings. From this result, we deduce that Newton’s method converges within a finite number of iterations over any semiring which is “collapsed at some k
On Fixed Point Equations over Commutative Semirings
, 2007
"... Fixed point equations x = f(x) overωcontinuous semirings can be seen as the mathematical foundation of interprocedural program analysis. The sequence 0, f(0), f 2 (0),...converges to the least fixed point μf. The convergence can be accelerated if the underlying semiring is commutative. We show tha ..."
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Cited by 19 (10 self)
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Fixed point equations x = f(x) overωcontinuous semirings can be seen as the mathematical foundation of interprocedural program analysis. The sequence 0, f(0), f 2 (0),...converges to the least fixed point μf. The convergence can be accelerated if the underlying semiring is commutative. We show
AN IDEALBASED ZERODIVISOR GRAPH OF A COMMUTATIVE SEMIRING
, 2009
"... There is a natural graph associated to the zerodivisors of a commutative semiring with nonzero identity. In this article we essentially study zerodivisor graphs with respect to primal and nonprimal ideals of a commutative semiring R and investigate the interplay between the semiringtheoretic p ..."
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There is a natural graph associated to the zerodivisors of a commutative semiring with nonzero identity. In this article we essentially study zerodivisor graphs with respect to primal and nonprimal ideals of a commutative semiring R and investigate the interplay between the semiring
Results 1  10
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169