An ordered semigroup is a structure S = 〈S, ·,≤〉 with a binary operation · that is associative and a partial ordering ≤ that is compatible with the binary operation. For a given congruence relation θ of the semigroup S = 〈S, ·〉 the quotient structure S/θ = 〈S/θ, , 〉 is not in general an ordered semigroup. In this paper we study quotients of ordered semigroups. We first define a special type of ...

We compute the Hilbert series of graded algebra real regular functions on a linear symplectic quotient by 2-torus as well first four coefficients Laurent expansion this at $$t = 1$$ . describe an algorithm to in explicit examples.

Let G be a locally compact group, let L1(G) be its group algebra, let M(G) be its usual measure algebra, let L1(G)∗∗ be the second dual of L1(G) with an Arens product, and let LUC(G)∗ be the conjugate of the space LUC(G) of bounded, left uniformly continuous, complex-valued functions on G with an Arens-type product. We find all the finite-dimensional left ideals of these algebras. We deduce tha...

Quotient is a basic operation of formal languages, which plays key role in the construction minimal deterministic finite automata (DFA) and universal automata. In this paper, we extend to power series systemically investigate its implications study weighted particular, define two quotient operations for are called (left or right) quotients residuals respectively. Algebraic properties closure (w...

A characterization of the quotient proximity is given. It is used to find necessary and sufficient conditions for every proximity map on a space to be a topological quotient map. It is shown that a separated proximity space is compact iff every /7-map on X with separated range is a proximity quotient map. Introduction. In 1959 Katetov [3] introduced proximity quotient maps. They have since been...

Let $R$ be a Noetherian local ring. We prove that is regular of dimension at most four if, and only every prime ideal, defining Gorenstein quotient ring, syzygetic. deduce characterization these rings in terms the Andr\'e-Quillen homology.

In this paper, we extend the notion of tree language quotients to bottom-up quotients. Instead of computing the residual of a tree language from top to bottom and producing a list of tree languages, we show how to compute a set of k-ary trees, where k is an arbitrary integer. We define the quotient formula for different combinations of tree languages: union, symbol products, compositions, itera...

A question which is frequently put to members of the Division of Special Education of The Board of Public Education, School District of Philadelphia, by visiting psychologists and educators is an inquiry as to how placement of children in Orthogenic Backward Classes, i.e., classes for the education of children who can not function adequately in the regular classes, is determined. All too freque...

A language L over an alphabet Σ is suffix-convex if, for any words x, y, z ∈ Σ∗, whenever z and xyz are in L, then so is yz. Suffixconvex languages include three special cases: left-ideal, suffix-closed, and suffix-free languages. We examine complexity properties of these three special classes of suffix-convex regular languages. In particular, we study the quotient/state complexity of boolean o...