In this paper we study the notions of cogenerator and subdirectlyirreducible in the category of S-poset. First we give somenecessary and sufficient conditions for a cogenerator $S$-posets.Then we see that under some conditions, regular injectivityimplies generator and cogenerator. Recalling Birkhoff'sRepresentation Theorem for algebra, we study subdirectlyirreducible S-posets and give this theo...

In this work we solve the following problem: Characterize the subclasses of implication algebras that can be axiomatized by sentences of the form 89! ^ p = q. In the process we obtain a representation result for …nite implication algebras, and as a by-product of our solution a number of interesting classes of implication algebras arise. We also obtain a characterization of the congruence permut...

The main goal of this paper is to introduce and investigate the related theory on monadic effect algebras. First, we design axiomatic system existential quantifiers algebras then use it give definition universal quantifier Then, relatively complete subalgebra prove that there exists a one-to-one correspondence between set all subalgebras. Moreover, characterize generated formula ideals Riesz co...

we consider a 2-dimensional representation of the hecke algebra h(g7; u), whereg7 is the complex re ection group and u is the set of indeterminatesu = (x1; x2; y1; y2; y3; z1; z2; z3):after specializing the indetrminates to non zero complex numbers, we then determine a nec-essary and sucient condition that guarantees the irreducibility of the complex specializationof the representation of the ...

CARL FAITH All rings considered are commutative with unit. A ring R is SISI (in Vámos' terminology) if every subdirectly irreducible factor ring R/I is self-injective . SISI rings include Noetherian rings, Morita rings, and almost maximal valuation rings ([Vil) . In [F3] we raised the question of whether a polynomial ring R[-1 over a SISI ring R is again SISI . In this paper we show this is not...

A semiring variety is d-semisimple if it is generated by the distributive lattice of order two and a finite number of finite fields. A d-semisimple variety V = HSP{B2, F1, . . . , Fk} plays the main role in this paper. It will be proved that it is finitely based, and that, up to isomorphism, the two-element distributive lattice B2 and all subfields of F1, . . . , Fk are the only subdirectly irr...

Abstract In this paper, we study the class of modules with fusion and implication based over distributive lattices , or FIDL - for short. We introduce concepts FIDL-subalgebra FIDL-congruence as well notions simple subdirectly irreducible FIDL-modules. give a bi-sorted Priestley-like duality FIDL-modules moreover, an application such duality, provide topological bi-spaced description FIDL-congr...

Let L1 be a finite simple sloop of cardinality n or the 8-element sloop. In this paper, we construct a subdirectly irreducible (monolithic) sloop L = 2⊗αL1 of cardinality 2n, for each n ≥ 8, with n ≡ 2 or 4 (mod 6), in which each proper homomorphic image is a Boolean sloop. Quackenbush [12] has proved that the variety V (L1) generated by a finite simple planar sloop L1 covers the smallest nontr...

Let A be a 4nitely generated variety of Heyting algebras and let SI(A) be the class of subdirectly irreducible algebras in A. We prove that A is dually equivalent to a category of functors from SI(A) into the category of Boolean spaces. The main tool is the theory of multisorted natural dualities. c © 2002 Elsevier Science B.V. All rights reserved. MSC: Primary: 06D20; 06D50; secondary: 08C05; ...

We give a representation of distributive lattices with the existential quantifier in terms of spectral spaces, which is an alternative to Cignoli’s representation in terms of Priestley spaces. Then we describe dual spectral spaces of subdirectly irreducible and simple Q-distributive lattices and prove that the variety QDist of Q-distributive lattices does not have the congruence extension prope...