Let n be a positive integer and let n = {1, . . . , n}. Let R be the set of all oneto-one maps σ with domain I (σ ) ⊆ n and range J (σ) ⊆ n. If i ∈ I (σ ) let iσ denote the image of i under σ . There is an associative product (σ, τ ) → στ on R defined by composition of maps: i(στ)= (iσ )τ if i ∈ I (σ ) and iσ ∈ I (τ ). Thus the domain I (στ) consists of all i ∈ I (σ ) such that iσ ∈ I (τ ). The...

In this paper, we give some characterizations of intraregular semigroups by the properties of their (∈,∈ ∨qk)-fuzzy right ideals, (∈,∈ ∨qk)-fuzzy left ideals, (∈,∈ ∨qk)-fuzzy interior ideals, (∈,∈ ∨qk)fuzzy bi-ideals and (∈,∈ ∨qk)-fuzzy generalized bi-ideals. 2010 AMS Classification: 03E72, 20M12

We investigate the class of quasitrivial semigroups and provide various characterizations of the subclass of quasitrivial and commutative semigroups as well as the subclass of quasitrivial and order-preserving semigroups. We also determine explicitly the sizes of these classes when the semigroups are defined on finite sets. As a byproduct of these enumerations, we obtain several new integer seq...

This paper studies automatic structures for subsemigroups of Baumslag–Solitar semigroups (that is, semigroups presented by ⟨x, y | (yx, xy)⟩ where m,n ∈ N). A geometric argument (a rarity in the field of automatic semigroups) is used to show that if m > n, all of the finitely generated subsemigroups of this semigroup are [right-] automatic. If m < n, all of its finitely generated subsemigroups ...

We prove that, for any n, the monoid of all $$n \times n$$ supertropical matrices extending tropical satisfies nontrivial semigroup identities; in particular, such triangular admit exactly same identities satisfied by matrices. These are carried over to labeled-weighted digraphs with double arcs.

solubility of high molecular weight n-paraffins in supercritical carbon dioxide has been a matter of interest to many researchers. however, not sufficient solubility experimental data are available although the methods by which the experimental data are obtained have many varieties. utilizing cubic equations of state is an effective method for solubility prediction of n-paraffins in supercritic...

decomposability of an algebraic structure into the :union: of its sub-structures goes back to g. scorza&apos;s theorem of 1926 for groups. an analogue of this theorem for rings has been recently studied by a. lucchini in 2012. on the study of this problem for non-group semigroups, the first attempt is due to clifford&apos;s work of 1961 for the regular semigroups. since then, n.p. mukherjee in ...

We consider the semigroup on L 1 (IR n) deened by the nonlinear transport equation for the scalar s @ t s + div(f(s) u) = 0 in (0; 1)I R n for given velocity eld u. We show that this nonlinear semigroup is HH older continuous for t > 0 in the uniform operator topology, provided the graph of f has no linear segments. This continuity property | which expresses a regularizing eeect of the nonlinea...

We analyse a stack protocol of the Capetanakis-Tsybakov-Mikhailov type for resolving collisions in a random multiple-access channel. We obtain a functional equation for the generating function of the expected collision resolution interval (CRI) durations, which is non-local with a noncommutative iteration semigroup. Using Mellin transform techniques and geometric properties of the iteration sem...

The Schur-Szegö composition of two polynomials of degree ≤ n introduces an interesting semigroup structure on polynomial spaces and is one of the basic tools in the analytic theory of polynomials, see [5]. In the present paper we show how it interacts with the stratification of polynomials according to the multiplicities of their zeros and we present the induced semigroup structure on the set o...