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Wehrung, Friedrich

It is well known that the real spectrum of any commutative unital ring, and the ℓ-spectrum of any Abelian lattice-ordered group with order-unit, are all completely normal spectral spaces. We prove the following results: (1) Every real spectrum can be embedded, as a spectral subspace, into some ℓ-spectrum. (2) Not every real spectrum is an ℓ-spectru...

Rump, Wolfgang
Published in
Mathematica Slovaca

Every semifield of non-zero characteristic is either a field of prime characteristic or a semifield of characteristic 1. Semifields of characteristic 1 are equivalent to abelian lattice-ordered groups. It is proved that such a semifield A is algebraically closed if and only if the pure equations xn = a and certain quadratic equations are solvable i...

Rump, Wolfgang Yang, Yichuan
Published in
Algebra universalis

L-algebras are related to algebraic logic and quantum structures. They were introduced by the first author [J. Algebra 320 (2008)], where a self-similar closure S(X) of any L-algebra X was employed to derive a criterion for X to be representable as an interval in a lattice-ordered group. In the present paper, this criterion is improved without usin...

Boccuto, Antonio Riečan, Beloslav
Published in
Mathematica Slovaca

Some extension theorems for l-group-valued M-measures are proved.

Buşneag, Dumitru Piciu, Dana
Published in
algebra universalis

The aim of the present paper is to define the localization MV-algebra of an MV-algebra A with respect to a topology ℱ on A; also, following the categorical equivalence between the category of lu-groups and the category of MV-algebras, we define the analogous notion for lu-groups. In Section 5 we prove that the maximal MV-algebra of quotients (defin...

Rachůnek, Jiří
Published in
Order

By the Holland Representation Theorem, every lattice ordered group (l-group) is isomorphic to a subalgebra of the l-group of automorphisms of a chain. Since weakly associative lattice groups (wal-groups) and tournaments are non-transitive generalizations of l-groups and chains, respectively, the problem concerning the possibility of representation ...