If one of the axioms in ring, namely inverse axiom addition operation, is omitted, it will produce another algebraic structure, a semiring. Analogous to there are zero elements, ideal (left/right) semiring, and cross product semiring ideal. The analog fuzzy has (left/right), associated with membership value. This paper discuss cross-product two (more) ideals from Furthermore, always be But conv...

The Semiring Constraint Satisfaction Problem (SCSP) framework is a popular approach for the representation of partial constraint satisfaction problems. In this framework preferences (semiring values) can be associated with tuples of values of the variable domains. Bistarelli et al. [1] define an abstract solution to a SCSP which consists of the best set of solution tuples for the variables in t...

We define rationally additive semirings that are a generalization of (ω)complete and (ω-)continuous semirings. We prove that every rationally additive semiring is an iteration semiring. Moreover, we characterize the semirings of rational power series with coefficients in N∞, the semiring of natural numbers equipped with a top element, as the free rationally additive semirings.

We present pumping lemmas for five classes of functions definable by fragments weighted automata over the min-plus semiring, max-plus semiring and natural numbers. As a corollary we show that hierarchy unambiguous, finitely-ambiguous, polynomially-ambiguous automata, full class is strict semirings.

There is a natural graph associated to the zero-divisors of a commutative semiring with non-zero identity. In this article we essentially study zero-divisor graphs with respect to primal and non-primal ideals of a commutative semiring R and investigate the interplay between the semiring-theoretic properties of R and the graph-theoretic properties of ΓI(R) for some ideal I of R. We also show tha...

Let be a commutative semiring. A semimodule over semiring is fully prime if each proper subsemimodule of prime. This research aims to investigate the relationship between direct sum subsemimodules and , semimodule.

The tropical semiring M consists of the set of natural numbers extended with innnity, equipped with the operations of taking minimums (as semiring addition) and addition (as semiring multiplication). We use factorization forests to prove niteness results related to semi-groups of matrices over M. Our method is used to recover results of Hashiguchi, Leung and the author in a uniied combinatorial...

We introduce the notion of a generalized semi-ideal in a ternary semiring. Various examples to establish a relationship between ideals, bi-ideals, quasi-ideals and generalized semi-ideals are furnished. A criterion for a commutative ternary semiring without any divisors of zero to a ternary division semiring is given. AMS Mathematics Subject Classification (2010): 16Y60, 16Y99

We consider tree automata with costs over semirings in the sense of (Seidl, 1994). We define the concept of a finitely factorizing semiring and of a monotonic semiring, both as the generalization of well-known particular semirings, and show that the costfiniteness of tree automata with costs over finitely factorizing and monotonic semirings is decidable. We show that, for tree automata with cos...