Displaying similar documents to “Subdirectly irreducible quasi-modal algebras.”

Discriminator varieties of Boolean algebras with residuated operators

Peter Jipsen (1993)

Banach Center Publications

Similarity:

The theory of discriminator algebras and varieties has been investigated extensively, and provides us with a wealth of information and techniques applicable to specific examples of such algebras and varieties. Here we give several such examples for Boolean algebras with a residuated binary operator, abbreviated as r-algebras. More specifically, we show that all finite r-algebras, all integral r-algebras, all unital r-algebras with finitely many elements below the unit, and all commutative...

On connections between information systems, rough sets and algebraic logic

Stephen Comer (1993)

Banach Center Publications

Similarity:

In this note we remark upon some relationships between the ideas of an approximation space and rough sets due to Pawlak ([9] and [10]) and algebras related to the study of algebraic logic - namely, cylindric algebras, relation algebras, and Stone algebras. The paper consists of three separate observations. The first deals with the family of approximation spaces induced by the indiscernability relation for different sets of attributes of an information system. In [3] the family of closure...

On the existence of prime ideals in Boolean algebras

Jörg Flum (1999)

Banach Center Publications

Similarity:

Rasiowa and Sikorski [5] showed that in any Boolean algebra there is an ultrafilter preserving countably many given infima. In [3] we proved an extension of this fact and gave some applications. Here, besides further remarks, we present some of these results in a more general setting.

Quasi-modal algebras

Sergio A. Celani (2001)

Mathematica Bohemica

Similarity:

In this paper we introduce the class of Boolean algebras with an operator between the algebra and the set of ideals of the algebra. This is a generalization of the Boolean algebras with operators. We prove that there exists a duality between these algebras and the Boolean spaces with a certain relation. We also give some applications of this duality.

Subdirect decompositions of algebras from 2-clone extensions of varieties

J. Płonka (1998)

Colloquium Mathematicae

Similarity:

Let τ:F → ℕ be a type of algebras, where F is a set of fundamental operation symbols and ℕ is the set of nonnegative integers. We assume that |F|≥2 and 0 ∉ (F). For a term φ of type τ we denote by F(φ) the set of fundamental operation symbols from F occurring in φ. An identity φ ≉ ψ of type τ is called clone compatible if φ and ψ are the same variable or F(φ)=F(ψ)≠ . For a variety V of type τ we denote by V c , 2 the variety of type τ defined by all identities φ ≉ ψ from Id(V) which are either...

Program Algebra over an Algebra

Grzegorz Bancerek (2012)

Formalized Mathematics

Similarity:

We introduce an algebra with free variables, an algebra with undefined values, a program algebra over a term algebra, an algebra with integers, and an algebra with arrays. Program algebra is defined as universal algebra with assignments. Programs depend on the set of generators with supporting variables and supporting terms which determine the value of free variables in the next state. The execution of a program is changing state according to successor function using supporting terms. ...

Weak products of universal algebras

Ildikó Sain (1993)

Banach Center Publications

Similarity:

Weak direct products of arbitrary universal algebras are introduced. The usual notion for groups and rings is a special case. Some universal algebraic properties are proved and applications to cylindric and polyadic algebras are considered.