Products in almost -algebras
Let be a uniformly complete almost -algebra and a natural number . Then is a uniformly complete semiprime -algebra under the ordering and multiplication inherited from with as positive cone.
Projektive geordnete Moduln und n-fache Erweiterungen geordneter Moduln.
Pseudocomplements in sum-ordered partial semirings
We study a particular way of introducing pseudocomplementation in ordered semigroups with zero, and characterise the class of those pseudocomplemented semigroups, termed g-semigroups here, that admit a Glivenko type theorem (the pseudocomplements form a Boolean algebra). Some further results are obtained for g-semirings - those sum-ordered partially additive semirings whose multiplicative part is a g-semigroup. In particular, we introduce the notion of a partial Stone semiring and show that several...
Putting together Lukasiewicz and product logics.
In this paper we investigate a propositional fuzzy logical system LΠ which contains the well-known Lukasiewicz, Product and Gödel fuzzy logics as sublogics. We define the corresponding algebraic structures, called LΠ-algebras and prove the following completeness result: a formula φ is provable in the LΠ logic iff it is a tautology for all linear LΠ-algebras. Moreover, linear LΠ-algebras are shown to be embeddable in linearly ordered abelian rings with a strong unit and cancellation law.
Quelques propriétés des anneaux dont un sous-demi-groupe multiplicatif est un -demi-groupe
Rechtsteilweise geordnete Halbgruppen
Rings and Partly Ordered Systems.
Rings Satisfying a Not-Necessarily Transitive Relation.
-Rings and -Porings
-rings are commutative rings whose factor rings modulo prime ideals are valuation rings. -rings occur most naturally in connection with partially ordered rings (= porings) and have been studied only in this context so far. The present note first develops the theory of -rings systematically, without assuming the presence of a partial order. Particular attention is paid to the question of axiomatizability (in the sense of model theory). Partially ordered -rings (-porings) are introduced, and...
Semejanzas en f-anillos.
Semimodules over ordered rings.
Singular operations on algebras (generalized contractions)
Sobre las isometrías de los grupos y anillos reticulados.
El contenido de este trabajo tiene un objetivo fundamental: el estudio, clasificación y caracterización de las isometrías de un grupo reticulado. Se introducen los conceptos de grupo de isometrías M(G) de un grupo reticulado G, grupo de simetrías homogéneas H(G) y traslaciones T(G). Se estudia primero el caso elemental de los grupos totalmente ordenados y utilizando luego las representaciones de los grupos (y f-anillos) en un producto de totalmente ordenados, se introduce el concepto de conjunto...
Some aspects of radical theory for fully ordered Abelian groups
Some comments and examples on generation of (hyper-)archimedean -groups and -rings
This paper systematizes some theory concerning the generation of -groups and reduced -rings from substructures. We are particularly concerned with archimedean and hyperarchimedean groups and rings. We discuss the process of adjoining a weak order unit to an -group, or an identity to an -ring and find significant contrasts between these cases. In -groups, hyperarchimedeanness and similar properties fail to pass from generating structures to the structures that they generate, as illustrated by...
Spaces in which all prime -ideals of are minimal or maximal
Quasi -spaces are defined to be those Tychonoff spaces such that each prime -ideal of is either minimal or maximal. This article is devoted to a systematic study of these spaces, which are an obvious generalization of -spaces. The compact quasi -spaces are characterized as the compact spaces which are scattered and of Cantor-Bendixson index no greater than 2. A thorough account of locally compact quasi -spaces is given. If is a cozero-complemented space and every nowhere dense zeroset...
Spectra of weakly associative lattice rings
Strictly order primal algebras.
Strong amalgamations of lattice ordered groups and modules.
Structure of ordered semirings.