2024/02/15 by A. R. Rajan, Rajan, A. R., S. Sheena +3
Computer Science · Decision Sciences · #Advanced Algebra and Logic #FOS: Mathematics #Fuzzy and Soft Set Theory #Group Theory (math.GR) #Rings and Algebras (math.RA)
paper · pdf · doi:10.48550/arxiv.2402.10103
openalex publication_date 2024/02/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Much study has been done on semigroups which are unions of groups. There are several ways in which a union of groups can be made into a semigroup in which each of the component groups arises as subgroups of the constructed semigroup. An important class of such unions is a semilattice of groups. Group semirings are semirings (G,+,⋅ ) where (G,⋅ ) is a group and (G,+) is a left zero semigroup. We consider construction of semirings from classes of group semirings \Gα:α∈ D \ indexed by a distributive lattice D. It is shown that if S=∪\Gα\ is a strong distributive lattice of group semirings Gα then the multiplicative semigroup (S,⋅) of the semiring (S,+,⋅) is a Clifford semigroup and the additive semigroup (S,+) is a left normal band. Further in this case all the groups Gα are mutually isomorphic.