Flatness of Semimodules over Semirings
by
Y. Katsov
Department of Mathematics and Computer Science, Hanover College, Hanover, Indiana

In the talk, there will be considered tensor product bifunctors in the context of semimodules over semirings, defined in such a fashion that they become left adjoints of the Hom functors (see, for example, Y. Katsov, Tensor products and injective envelopes of semimodules over additively regular semirings, Algebra Colloquium 4:2 (1997) 121-131). As usual, a left semimodule A over a semiring R is said to be flat if the tensor multiplication by A preserves all finite limits. On the other hand, A is called L-flat if it is a filtered colimit of finitely generated free semimodules. Using Shannon's characterization of L-flatness for algebraic categories, we establish that in the setting of semimodules over semirings both concepts - flatness and L-flatness - coincide (Govorov-Lazard's theorem for the varieties of semimodules over semirings). Then, there will be described flat semimodules over finite Boolean algebras, in particular 0-flat semilattices, as well as commutative semirings over which all semimodules are flat.

Date received: December 22, 2001

Copyright © 2001 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # caig-09.