Let R be a ring. An element a in R is called left morphic (Nicholson and Sánchez Campos, 2004a) if l a R/Ra, where l a denotes the left annihilator of a in R. The ring itself is called a left morphic ring if every element is left morphic. Left morphic rings were first introduced by Nicholson and Sánchez Campos (2004a) and were discussed in great detail there and in Nicholson and Sánchez Campos ...

We characterise quasivarieties and varieties of ordered algebras categorically in terms of regularity, exactness and the existence of a suitable generator. The notions of regularity and exactness need to be understood in the sense of category theory enriched over posets. We also prove that finitary varieties of ordered algebras are cocompletions of their theories under sifted colimits (again, i...

What I intend to show in this short paper is how one can translate in relational terms the concepts of deducibility and exactness which are the result of a sequence of works on homology theory and algebraic topology. As we shall see, we shall obtain as a final product the possibility to associate to an arbitrary binary relation R a difunctional relation R contained in R, in contrast with the di...

THEOREM I. Let X be a small category. Then the following assertions are equivalent: (1) The inverse limit proj limx: AB-^AB is exact (2) For every abelian category SÏ with exact direct products y the inverse limit proj lim* : %—»3I is exact. (3) Every connected component Y of X contains an object y together with an endomorphism eÇz Y (y, y) such that the following properties are satisfied: (i) ...

Uninorms are important generalizations of triangular norms and conorms, with a neutral element lying anywhere in the unit interval, and left (right) semi-uninorms are non-commutative and non-associative extensions of uninorms. In this paper, we firstly introduce the concepts of left and right semi-uninorms on a complete lattice and illustrate these notions by means of some examples. Then, we la...

Our investigation of coalgebras over commutative rings R is based on the close relationship between comodules over a coalgebra C and modules over the dual algebra C∗. If C is projective as an R-module the category of right C-comodules can be identified with the category σ[C∗C] of left C∗-modules which are subgenerated by C. In this context semiperfect coalgebras are described by results from mo...

Robin Harte and David Larson The first author was partially supported by Enterprise Ireland grant number IC/2001/027 Abstract We offer a perturbation theory for finite ascent and descent properties of bounded operators. There are various degrees of “skew exactness” ([10];[7] (10.9.0.1), (10.9.0.2)) between compatible pairs of operators, bounded and linear between normed spaces: 1. Definition Su...

Statistical methods for automatically identifying de pendent word pairs i e dependent bigrams in a cor pus of natural language text have traditionally been performed using asymptotic tests of signi cance This paper suggests that Fisher s exact test is a more ap propriate test due to the skewed and sparse data sam ples typical of this problem Both theoretical and experimental comparisons between...