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1

Discriminator varieties of double-Heyting algebras

Taylor C. J.

Reports on Mathematical Logic

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2016

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Vol. 51

3--14

EN

We prove that a variety of double-Heyting algebras is a discriminator variety if and only if it is semisimple if and only if it has equationally denable principal congruences. The result also applies to the class of Heyting algebras with a dual pseudocomplement operation and to the class of regular double p-algebras.

2

Involutory BE-algebras

Borzooei R. A., Borumand Saeid A., Ameri R., Rezaei A.

Journal of Mathematics and Applications

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2014

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Vol. 37

13--26

EN

This paper is devoted to the study of some structural properties of bounded and involutory BE-algebras and investigate the relationship between them. We construct a commutative monoid by definition of proper operation in an involutory BE-algebra. Some rules of calculus for BE-algebras with a semi-lattice structure are provided. Many results related to the natural order of a BE-algebras were found. Finally, we show that an involutory bounded BE-algebra X is semi-simple.

3

Upper bounds on the sizes of finitely generated algebras

Berman J.

Demonstratio Mathematica

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2011

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Vol. 44, nr 3

447-471

EN

We present an upper bound for the cardinality of any n-generated algebra in a locally finite variety V of algebras. This upper bound depends only on some fundamental numerical invariants of the n-generated subdirectly irreducible algebras in V. A theorem characterizing those varieties that contain algebras whose cardinalities achieve the upper bound is proved. Several explicit methods for computing the exact values of these invariants are described. The final section contains detailed concrete examples illustrating applications of the characterization theorem and of the various methods for computing the upper bound.

4

On the Krull property in topological algebras

Haralampidou M.

Annales Societatis Mathematicae Polonae. Seria 1: Commentationes Mathematicae

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2006

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Vol. 46, [Z] 2

141-162

EN

We introduce Krull topological algebras. In particular, we characterize the Krull property in some special classes of topological algebras. Connections with the theory of semisimple annihilator Q0-algebras are given. Relative to this, an investigation on the relationship between Krull and (weakly) regular (viz. modular) annihilator algebras is considered. Subalgebras of certain Krull algebras are also presented. Moreover, conditions are supplied under which the Krull (resp. Q'-) property is preserved via algebra morphisms. As an application, we show that the quotient of a Krull Q'-algebra, modulo a 2-sided ideal, is a topological algebra of the same type. Finally, we study the Krull property in a certain algebra-valued function topological algebra.

5

Classification of locally m-convex algebras through Le Page condition

Haralampidou M.

Annales Societatis Mathematicae Polonae. Seria 1: Commentationes Mathematicae

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2004

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Vol. 44, nr 2

255-269

EN

We classify certain locally m-convex algebras, in terms of Le Page condition. In particular, we show that a unital locally m-convex algebra E satisfies Le Page condition and has no non-trivial idempotents if and only if E = C , within a topological algebra isomorphism. Besides, the algebra Cm<-E^ ( pointwise defined operations and cartesian product topology) characterizes all complex unital complete locally m-convex Le Page Q'-algebras E which have a discrete spectrum VJl(E). Hence, the algebra in question is not finite dimensional, by contrast with the classical case, where a unital complex Banach algebra satisfying Le Page condition is finite dimensional. The first principal Wedderburn structure theorem, for certain particular locally m-convex algebras satisfying the generalized Le Page condition is obtained.