scholarly journals On the coset structure of a skew lattice

2011 ◽  
Vol 44 (4) ◽  
Author(s):  
João Pita Costa
Keyword(s):  
Algebraic Theory ◽  
Skew Lattice ◽  
Skew Lattices ◽  
Green’S Relation

AbstractThe class of skew lattices can be seen as an algebraic category. It models an algebraic theory in the category of sets where the Green’s relation

scholarly journals On residuated skew lattices

2019 ◽  
Vol 27 (1) ◽  
pp. 245-268
Author(s):  
Arsham Borumand Saeid ◽  
Roghayeh Koohnavard
Keyword(s):  
Congruence Relation ◽  
Residuated Lattice ◽  
Deductive System ◽  
Quotient Algebra ◽  
Skew Lattice ◽  
Skew Lattices ◽  
Green’S Relation

Abstract In this paper, we define residuated skew lattice as non-commutative generalization of residuated lattice and investigate its properties. We show that Green’s relation 𝔻 is a congruence relation on residuated skew lattice and its quotient algebra is a residuated lattice. Deductive system and skew deductive system in residuated skew lattices are defined and relationships between them are given and proved. We define branchwise residuated skew lattice and show that a conormal distributive residuated skew lattice is equivalent with a branchwise residuated skew lattice under a condition.

scholarly journals On the Coset Category of a Skew Lattice

2014 ◽  
Vol 47 (3) ◽  
Author(s):  
João Pita Costa
Keyword(s):  
Sufficient Conditions ◽  
Skew Lattice ◽  
Skew Lattices ◽  
Structure Decomposition ◽  
Original Approach

AbstractSkew lattices are noncommutative generalizations of lattices. The coset structure decomposition is an original approach to the study of these algebras describing the relation between its rectangular classes. In this paper, we will look at the category determined by these rectangular algebras and the morphisms between them, showing that not all skew lattices can determine such a category. Furthermore, we will present a class of examples of skew lattices in rings that are not strictly categorical, and present sufficient conditions for skew lattices of matrices in rings to constitute ^-distributive skew lattices

Affine algebraic sets relative to an algebraic theory

1999 ◽  
Vol 65 (1-2) ◽  
pp. 54-76 ◽  
Author(s):  
Yves Diers
Keyword(s):  
Algebraic Theory ◽  
Algebraic Sets

The Algebraic Theory of Semigroups, Vol. I

1964 ◽  
Vol 48 (363) ◽  
pp. 122
Author(s):  
W. D. Munn ◽  
A. H. Clifford ◽  
G. B. Preston
Keyword(s):  
Algebraic Theory
Sign in / Sign up

Export Citation Format

Share Document