Multiplicatively idempotent semirings with annihilator condition. II
Year: 2025
Type: article
Abstract: The article continues the study of multiplicatively idempotent semirings with the annihilation condition. It is proven that for multiplicatively idempotent semirings with zero the annihilation condition is equivalent to the equalizing property (Theorem 1). New conditions are obtained (Rickart property, properties of a simple spectrum, and others) under which a multiplicatively idempotent semiring is isomorphic to the direct product of a Boolean ring and a generalized Boolean lattice (Theorems 2 and 3). Some other statements have also been proved, examples have been given, and explanatory remarks have been made.
Source: Russian Mathematics
Author: E. M. Vechtomov
Institution: Vyatka State University
Language: English
Topic: Rings, Modules, and Algebras
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
OpenAlex ID: W4411838574