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Deductive systems of BCK-algebras

Sergio A. Celani (2004)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

In this paper we shall give some results on irreducible deductive systems in BCK-algebras and we shall prove that the set of all deductive systems of a BCK-algebra is a Heyting algebra. As a consequence of this result we shall show that the annihilator F * of a deductive system F is the the pseudocomplement of F . These results are more general than that the similar results given by M. Kondo in [7].

Degeneration of Schubert varieties of S L n / B to toric varieties

Raika Dehy, Rupert W.T. Yu (2001)

Annales de l’institut Fourier

Using the polytopes defined in an earlier paper, we show in this paper the existence of degeneration of a large class of Schubert varieties of S L n to toric varieties by extending the method used by Gonciulea and Lakshmibai for a miniscule G / P to Schubert varieties in S L n .

Dimension in algebraic frames

Jorge Martinez (2006)

Czechoslovak Mathematical Journal

In an algebraic frame L the dimension, dim ( L ) , is defined, as in classical ideal theory, to be the maximum of the lengths n of chains of primes p 0 < p 1 < < p n , if such a maximum exists, and otherwise. A notion of “dominance” is then defined among the compact elements of L , which affords one a primefree way to compute dimension. Various subordinate dimensions are considered on a number of frame quotients of L , including the frames d L and z L of d -elements and z -elements, respectively. The more concrete illustrations...

Dimension in algebraic frames, II: Applications to frames of ideals in C ( X )

Jorge Martinez, Eric R. Zenk (2005)

Commentationes Mathematicae Universitatis Carolinae

This paper continues the investigation into Krull-style dimensions in algebraic frames. Let L be an algebraic frame. dim ( L ) is the supremum of the lengths k of sequences p 0 < p 1 < < p k of (proper) prime elements of L . Recently, Th. Coquand, H. Lombardi and M.-F. Roy have formulated a characterization which describes the dimension of L in terms of the dimensions of certain boundary quotients of L . This paper gives a purely frame-theoretic proof of this result, at once generalizing it to frames which are not necessarily...

Direct product decompositions of bounded commutative residuated -monoids

Ján Jakubík (2008)

Czechoslovak Mathematical Journal

The notion of bounded commutative residuated -monoid ( B C R -monoid, in short) generalizes both the notions of M V -algebra and of B L -algebra. Let A ̧ be a B C R -monoid; we denote by ( A ̧ ) the underlying lattice of A ̧ . In the present paper we show that each direct...

Direct product decompositions of infinitely distributive lattices

Ján Jakubík (2000)

Mathematica Bohemica

Let α be an infinite cardinal. Let 𝒯 α be the class of all lattices which are conditionally α -complete and infinitely distributive. We denote by 𝒯 σ ' the class of all lattices X such that X is infinitely distributive, σ -complete and has the least element. In this paper we deal with direct factors of lattices belonging to 𝒯 α . As an application, we prove a result of Cantor-Bernstein type for lattices belonging to the class 𝒯 σ ' .

Direct summands and retract mappings of generalized M V -algebras

Ján Jakubík (2008)

Czechoslovak Mathematical Journal

In the present paper we deal with generalized M V -algebras ( G M V -algebras, in short) in the sense of Galatos and Tsinakis. According to a result of the mentioned authors, G M V -algebras can be obtained by a truncation construction from lattice ordered groups. We investigate direct summands and retract mappings of G M V -algebras. The relations between G M V -algebras and lattice ordered groups are essential for this investigation.

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