Chain conditions on semirings.
Characterization of Regular Semirings
Characterizations of projective and -projective semimodules.
Clifford semifields
It is well known that a semigroup S is a Clifford semigroup if and only if S is a strong semilattice of groups. We have recently extended this important result from semigroups to semirings by showing that a semiring S is a Clifford semiring if and only if S is a strong distributive lattice of skew-rings. In this paper, we introduce the notions of Clifford semidomain and Clifford semifield. Some structure theorems for these semirings are obtained.
Commutative parasemifields finitely generated as semirings
Commutative semigroups that are simple over thein endomorphism semirings
Commutative semigroups with almost transitive endomorphism semirings
Commutative semigroups with few fully invariant congruences I.
Commutative semigroups with few fully invariant congruences II.
Completely positive matrices over Boolean algebras and their CP-rank
Drew, Johnson and Loewy conjectured that for n ≥ 4, the CP-rank of every n × n completely positive real matrix is at most [n2/4]. In this paper, we prove this conjecture for n × n completely positive matrices over Boolean algebras (finite or infinite). In addition,we formulate various CP-rank inequalities of completely positive matrices over special semirings using semiring homomorphisms.
Completeness criteria and invariants for operation and transformation algebras.
Congruence-free commutative semirings.
Congruences of pseudocomplemented algebras
Convexity theories 0 fin. Foundations.
In this paper we study big convexity theories, that is convexity theories that are not necessarily bounded. As in the bounded case (see [4]) such a convexity theory Γ gives rise to the category ΓC of (left) Γ-convex modules. This is an equationally presentable category, and we prove that it is indeed an algebraic category over Set. We also introduce the category ΓAlg of Γ-convex algebras and show that the category Frm of frames is isomorphic to the category of associative, commutative, idempotent...
Correction to "On the Radical of a Pseudo-Ring".
Decomposition of a semiring into division semirings
Derivations in some finite endomorphism semirings
The goal of this paper is to provide some basic structure information on derivations in finite semirings.
Die Lösung eines Problems von Havel
Distributive lattices of t-k-Archimedean semirings
A semiring S in 𝕊𝕃⁺ is a t-k-Archimedean semiring if for all a,b ∈ S, b ∈ √(Sa) ∩ √(aS). Here we introduce the t-k-Archimedean semirings and characterize the semirings which are distributive lattice (chain) of t-k-Archimedean semirings. A semiring S is a distributive lattice of t-k-Archimedean semirings if and only if √B is a k-ideal, and S is a chain of t-k-Archimedean semirings if and only if √B is a completely prime k-ideal, for every k-bi-ideal B of S.
Division Semirings with 1 + 1 = 1 .