The flat semirings with nilpotent multiplicative reducts
Abstract
In this paper, we focus on the variety NF3 generated by all flat semirings with 3-nilpotent multiplicative reducts. By introducing graph semirings, we characterize all subdirectly irreducible members of NF3. We prove that the variety NF3 has uncountably many subvarieties and show that every finitely generated subvariety of NF3 is a Cross variety. Moreover, we demonstrate that NF3 has a unique limit subvariety, which is generated by all acyclic graph semirings.
Fields of Study & Subjects
semigroups and automata theory
Polynomial and algebraic computation
Fuzzy and Soft Set Theory
Publication details
- Journal / source
- Communications in Algebra
- Pages
- 1–17
- Publication date
- 30 April 2026
- Language
- EN