Von Neumann Regular Semiring Ali, Alaa Hussein; Ali Alhossaini, Asaad Mohammed
Journal of physics. Conference series,
07/2020, Volume:
1591, Issue:
1
Journal Article
Peer reviewed
Open access
The aim of this action is a study and investigate "Von Neumann regular" semirings, some related concepts, e.g. reduced semirings; duo semiring, quasi-duo, and weakly duo semirings; regular, weakly ...regular and strongly regular semirings, also investigated. Some known results related to those concepts in rings were converted to semirings. Another aim of this paper is characterization Von Neumann Regular condition by the principal right ideal generated by an idempotent element.
In this paper, we introduce homological structure theory of semirings and CP-semirings — semirings all of whose cyclic semimodules are projective. We completely describe semisimple, Gelfand, ...subtractive, and anti-bounded, CP-semirings. We give complete characterizations of congruence-simple subtractive CP-semirings and congruence-simple anti-bounded semirings, which solve two earlier open problems for these classes of semirings. We also study in detail the properties of semimodules over Boolean algebras whose endomorphism semirings are CP-semirings; and, as a consequence of this result, we give a complete description of ideal-simple CP-semirings.
This paper investigates the concept (α, β) derivation on semiring and extend a few results of this map on prime semiring. We establish the commutativity of prime semiring and investigate when ...(α, β) derivation becomes zero.
The article explores research findings akin to Amitsur’s theorem, asserting that any derivation within a matrix ring can be expressed as the sum of an inner derivation and a hereditary derivation. In ...most results related to rings and semirings, Birkenmeier’s semicentral idempotents play a crucial role. This article is intended for PhD students, postdocs, and researchers.
In this article, we introduce and study V- and CI-semirings-semirings all of whose simple and cyclic, respectively, semimodules are injective. We describe V-semirings for some classes of semirings ...and establish some fundamental properties of V-semirings. We show that all Jacobson-semisimple V-semirings are V-rings. We also completely describe the bounded distributive lattices, Gelfand, subtractive, semisimple, and antibounded, semirings that are CI-semirings. Applying these results, we give complete characterizations of congruence-simple subtractive and congruence-simple antibounded CI-semirings which solve two earlier open problems for these classes of CI-semirings.
We show that there is an effectively given zero-sum-free commutative semiring S, contained as the subsemiring of nonnegative elements in an effectively given commutative ordered ring, for which there ...are no procedures deciding, given a weighted finite automaton over S, whether its support is the language of all words or whether its support is infinite. In particular, by a result of D. Kirsten (2011), since S is zero-sum-free and commutative, the support is recognizable by a classical finite automaton, but such an automaton or even just a pushdown automaton for its support cannot be constructed effectively.
•We construct an effectively given zero-sum-free commutative semiring S as a subsemiring of a commutative ordered ring.•It is undecidable, given a weighted finite automaton over S, whether its support is the language of all words.•It is also undecidable whether the support is infinite.•By a result of D. Kirsten (2011), the support is recognizable by a classical finite automaton.•But such an automaton or even just a pushdown automaton for its support cannot be constructed effectively.
We extend the concept of *-derivations of rings to a certain class of semirings called MA-semirings and establish some results on commutativity forced by the *-derivations satisfying different ...criteria. We specially focus on the results on certain conditions under which additive mappings become Jordan *-derivations.
In this paper, the notions of commutator and derivation in additively regular -semirings with (
, Г)-condition are introduced. We also characterize Jordan product for additively regular Г -semiring ...and establish some results which investigate the relationship between commutators, derivations and inner derivations. In 1957, E.C. Posner has shown that if there exists a non-zero centralizing derivation in a prime ring
, then
is commutative. This result is extended in the frame work of derivations of prime additively regular Г -semirings.
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