The injective tensor product of normal representable bimodules over von Neumann algebras is shown to be normal. The usual Banach module projective tensor product of central representable bimodules over an Abelian C∗-algebra is shown to be representable. A normal version of the projective tensor product is introduced for central normal bimodules.

We show that the term equivalence between MV-algebras and MV-semirings lifts to involutive residuated lattices a class of semirings called semirings. The semiring perspective leads necessary sufficient condition for interval [Formula: see text] be subalgebra an lattice, where is dualizing element. also import some results techniques semimodule theory in study this semirings, generalizing about ...

we investigate the relative cohomology and relative homology theories of $f$-gorenstein modules, consider the relations between classical and $f$-gorenstein (co)homology theories.