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- W3032832942 abstract "An incline S is a commutative semiring where r+1=1 for any r∈S. We note that the ideal lattice of an S-semimodule is naturally an S-semimodule and so is its congruence lattice when S is transitive. We prove that the categories of complete S-semimodules, together with dual functor, internal hom and tensor product, is a ⋆-autonomous category. We define the locally and globally maximal congruences which are related to Birkhoff subdirect product decomposition. We show that the categories of S-semimodules, algebraic S-semimodules and topological S-semimodules are equivalent. Finally, we get a sheaf representation of any S-semimodule." @default.
- W3032832942 created "2020-06-05" @default.
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- W3032832942 date "2020-12-01" @default.
- W3032832942 modified "2023-09-27" @default.
- W3032832942 title "Structure and representation of semimodules over inclines" @default.
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- W3032832942 doi "https://doi.org/10.1016/j.apal.2020.102844" @default.
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