Right-linear finite path overlapping TRS are shown to effectively preserve recognizability. The class of right-linear finite path overlapping TRS properly includes the class of linear generalized semi-monadic TRS and the class of inverse left-linear growing TRS, which are known to effectively preserve recognizability.

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In this paper, we consider the relationship between the equilibrium spreads and the liquidity supplier’s risk aversion coefficient, which represents the degree of risk aversion in a limit order market and a dealer market. Thus, we analyze which market is more liquid, the limit order market system or the dealer market system. It is concluded that the spread in a limit order market is not necessarily narrower than that in a dealer market, i.e., market liquidity depends on a liquidity supplier’s attitude to the risky asset.

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We introduce the notion of interval-valued fuzzy bi-ideals with respect to t-norm T* and s-norm S* and investigate some of the properties. The homomorphism image and inverse image are investigated. In particular, by the congruence relations on semigroups, new interval valued intuitionistic (S*, T*)-fuzzy bi-ideals are constructed.

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In this paper we show the way we pass from ordered semigroups to ordered Γ-semigroups. Moreover we show that, exactly as in ordered semigroups, in the results of ordered Γ-semigroups based on right (left) ideals, quasi-ideals and bi-ideals, points do not play any essential role, but the sets, which shows their pointless character. Under the methodology using in this paper, all the results of ordered semigroups can be transferred into ordered Γ-semigroups.

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Let R be a Noetherian ring and let Z(R) be the set of all zero-divisors of R. We denote by G(R) the simple graph whose vertices are elements of R and in which two distinct vertices x and y are joined by an edge if x−y is in Z(R). Let χ(R) be the chromatic number of the graph G(R). If χ(R) is finite, then R is an integral domain or R is a finite Artin ring. In the former case we have χ(R) = 1 and in the latter case we get χ(R) = max{|M1|, . . . , |Mt|} where M1, . . . ,Mt are all maximal ideals of R and |Mi| denotes the number of elements of the set Mi for i = 1, . . . , t.

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In this paper we first give a procedure by which we generate a filter by a subset in a transitive BE-algebra, and give some characterizations of Noetherian and Artinian BE-algebras. Next we give the construction of quotient algebra X/F of a transitive BE-algebra X via a filter F of X. Finally we discuss properties of Noetherian (resp. Artinian) BE-algebras on homomorphisms and prove that let X and Y be transitive BE-algebras, a mapping f : X → Y be an epimorphism. If X is Noetherian (resp. Artinian), then so does Y . Conversely suppose that Y and Ker(f) (as a subalgebra of X) are Noetherian (resp. Artinian), then so does X. Let X be a transitive BE-algebra and F a filter of X. If X is Noetherian (resp. Artinian), then so does the quotient algebra X/F.

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In this paper, we construct a 1-safe Petri net that generates all the binary n-vectors, possibly with repetitions.

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In this paper, using the concept of pseudoorder, we first prove that each ordered semigroup can be considered as a quotient of a free ordered semigroup. Then we give a characterization of free ordered semigroups.

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