On Flat Semimodules over Semirings |
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Authors: | Yefim Katsov |
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Institution: | (1) Department of Mathematics and Computer Science, Hanover College, 47243-0890 Hanover, IN, USA |
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Abstract: | The following analog of the characterization of flat modules has been obtained
for the variety of semimodules over a semiring R: A semimodule
RA is flat (i.e., the tensor
product functor – A preserves all finite limits) iff
A is L-flat (i.e., A
is a filtered colimit of finitely generated free semimodules). We also give new (homological) characterizations of
Boolean algebras and complete Boolean algebras within the classes of distributive lattices
and Boolean algebras, respectively, which solve two problems left open in 14]. It is also
shown that, in contrast with the case of modules over rings, in general for semimodules over
semirings the notions of flatness and mono-.atness (i.e., the tensor product functor – A
preserves monomorphisms) are different. |
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Keywords: | 16Y60 08B30 06A12 06E99 18A40 18G05 |
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