We introduce the notion of a standard system in order to deal with quasi-hereditary algebras. We shall prove that a necessary and sufficient condition for a finite dimensional algebra to be quasi-hereditary is the existence of a full and divisible standard system. As a further application, we obtain a sufficient condition for a standardly stratified algebra. To Roger Carter on his 65th birthday

In this paper, we investigate approximation of quasi-projection operators in Besov spaces B p,q, μ > 0, 1 ≤ p, q ≤ ∞. Suppose I is a countable index set. Let (φi)i∈I be a family of functions in Lp(IR), and let (φ̃i)i∈I be a family of functions in Lp̃(IR), where 1/p+ 1/p̃ = 1. Let Q be the quasi-projection operator given by

A set is said to be amorphous if it is innnite, but cannot be written as the disjoint union of two innnite sets. The possible structures which an amorphous set can carry were discussed in 5]. Here we study an analogous notion at the next level up, that is to say replacing nite/innnite by countable/uncountable, saying that a set is quasi-amorphous if it is uncountable, but is not the disjoint un...

Given an infinite Boolean algebra B, we find a natural class of ∅-definable equivalence relations EB such that every imaginary element from B is interdefinable with an element from a sort determined by some equivalence relation from EB . It follows that B together with the family of sorts determined by EB admits elimination of imaginaries in a suitable multisorted language. The paper generalize...

The Kemperman Structure Theorem (KST) yields a recursive description of the structure of a pair of finite subsets A and B of an abelian group satisfying |A + B| ≤ |A| + |B| − 1. In this paper, we introduce a notion of quasi-periodic decompositions and develop their basic properties in relation to KST. This yields a fuller understanding of KST, and gives a way to more effectively use KST in prac...

We investigate ways of representing ordered sets as algebras and how the order relation is reflected in the algebraic properties of the variety (equational class) generated by these algebras. In particular we consider two different but related methods for constructing an algebra with one binary operation from an arbitrary ordered set with a top element. The two varieties generated by all these ...

In this paper, using the idea of quasi-coincidence of a fuzzy point with a fuzzy set, the concept of (∈,∈ ∨q)fuzzy interior ideals in a Γ-semigroup has been introduced and some of their important related properties have been investigated. Characterizations of regular Γsemigroups, intra-regular Γ-semigroups, and semisimple Γ-semigroups in terms of (∈,∈ ∨q)-fuzzy interior ideals have also been ob...

The equation to be considered is Lny(t) + p(t)y((t)) = 0: The aim of this paper is to derive suucient conditions for property (A) of this equation. In the paper a result of D zurina 2] concerning asymptotic properties of the third order linear diierential equations with delay is extended to an n-th order delay diierential equation. We consider the diierential equation (1) L n y(t) + p(t)y((t)) ...

Parallel to the concept of quasi-separate continuity, we define a notion for quasi-oscillation of a mapping f : X × Y → R. We also introduce a topological game on X to approximate the oscillation of f . It follows that under suitable conditions, every quasi-separately continuous mapping f : X×Y → R has the Namioka property. An illuminating example is also given.