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A class of multiplicative lattices

Tiberiu Dumitrescu, Mihai Epure (2021)

Czechoslovak Mathematical Journal

We study the multiplicative lattices L which satisfy the condition a = ( a : ( a : b ) ) ( a : b ) for all a , b L . Call them sharp lattices. We prove that every totally ordered sharp lattice is isomorphic to the ideal lattice of a valuation domain with value group or . A sharp lattice L localized at its maximal elements are totally ordered sharp lattices. The converse is true if L has finite character.

A note on noninterpretability in o-minimal structures

Ricardo Bianconi (1998)

Fundamenta Mathematicae

We prove that if M is an o-minimal structure whose underlying order is dense then Th(M) does not interpret the theory of an infinite discretely ordered structure. We also make a conjecture concerning the class of the theory of an infinite discretely ordered o-minimal structure.

Axiomatizing omega and omega-op powers of words

Stephen L. Bloom, Zoltán Ésik (2004)

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

In 1978, Courcelle asked for a complete set of axioms and rules for the equational theory of (discrete regular) words equipped with the operations of product, omega power and omega-op power. In this paper we find a simple set of equations and prove they are complete. Moreover, we show that the equational theory is decidable in polynomial time.

Axiomatizing omega and omega-op powers of words

Stephen L. Bloom, Zoltán Ésik (2010)

RAIRO - Theoretical Informatics and Applications

In 1978, Courcelle asked for a complete set of axioms and rules for the equational theory of (discrete regular) words equipped with the operations of product, omega power and omega-op power. In this paper we find a simple set of equations and prove they are complete. Moreover, we show that the equational theory is decidable in polynomial time.

Constructions of cell algebras

Alfonz Haviar, Gabriela Monoszová (2005)

Mathematica Bohemica

A construction of cell algebras is introduced and some of their properties are investigated. A particular case of this construction for lattices of nets is considered.

Cyclically valued rings and formal power series

Gérard Leloup (2007)

Annales mathématiques Blaise Pascal

Rings of formal power series k [ [ C ] ] with exponents in a cyclically ordered group C were defined in [2]. Now, there exists a “valuation” on k [ [ C ] ] : for every σ in k [ [ C ] ] and c in C , we let v ( c , σ ) be the first element of the support of σ which is greater than or equal to c . Structures with such a valuation can be called cyclically valued rings. Others examples of cyclically valued rings are obtained by “twisting” the multiplication in k [ [ C ] ] . We prove that a cyclically valued ring is a subring of a power series ring k [ [ C , θ ] ] with...

Extensions of group retractions.

Byrd, Richard D., Lloyd, Justin T., Mena, Roberto A., Teller, J.Roger (1980)

International Journal of Mathematics and Mathematical Sciences

Lexicographic product decompositions of half linearly ordered loops

Milan Demko (2007)

Czechoslovak Mathematical Journal

In this paper we prove for an hl-loop Q an assertion analogous to the result of Jakubík concerning lexicographic products of half linearly ordered groups. We found conditions under which any two lexicographic product decompositions of an hl-loop Q with a finite number of lexicographic factors have isomorphic refinements.

Linear extensions of orders invariant under abelian group actions

Alexander R. Pruss (2014)

Colloquium Mathematicae

Let G be an abelian group acting on a set X, and suppose that no element of G has any finite orbit of size greater than one. We show that every partial order on X invariant under G extends to a linear order on X also invariant under G. We then discuss extensions to linear preorders when the orbit condition is not met, and show that for any abelian group acting on a set X, there is a linear preorder ≤ on the powerset 𝓟X invariant under G and such that if A is a proper subset of B, then A < B...

Modular atomic effect algebras and the existence of subadditive states

Zdena Riečanová (2004)

Kybernetika

Lattice effect algebras generalize orthomodular lattices and M V -algebras. We describe all complete modular atomic effect algebras. This allows us to prove the existence of ordercontinuous subadditive states (probabilities) on them. For the separable noncomplete ones we show that the existence of a faithful probability is equivalent to the condition that their MacNeille complete modular effect algebra.

On Butler B ( 2 ) -groups decomposing over two base elements

Clorinda de Vivo, Claudia Metelli (2009)

Commentationes Mathematicae Universitatis Carolinae

A B ( 2 ) -group is a sum of a finite number of torsionfree Abelian groups of rank 1 , subject to two independent linear relations. We complete here the study of direct decompositions over two base elements, determining the cases where the relations play an essential role.

On congruences and ideals of partially ordered quasigroups

Milan Demko (2008)

Czechoslovak Mathematical Journal

Some results concerning congruence relations on partially ordered quasigroups (especially, Riesz quasigroups) and ideals of partially ordered loops are presented. These results generalize the assertions which were proved by Fuchs in [5] for partially ordered groups and Riesz groups.

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