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 ...

It is known that classical logic CL is the single maximal consistent logic over intuitionistic logic Int, which is moreover the single one even over the substructural logic FLew. On the other hand, if we consider maximal consistent logics over a weaker logic, there may be uncountablymany of them. Since the subvariety lattice of a given variety V of residuated lattices is dually isomorphic to th...

We analyze involutions which prove several partition identities and describe them in a uniform fashion as projections of “natural” partition involutions along certain bijections. The involutions include those due to Franklin, Sylvester, Andrews, as well as few others. A new involution is constructed for an identity of Ramanujan, and analyzed in the same fashion. Introduction Combinatorial metho...

We introduce the decreasing proof order. It orders a conversion above another conversion if the latter is obtained by filling any peak in the former by a decreasing diagram. The result is developed in the setting of involutive monoids.

We confirm a conjecture of Bernstein-Lunts which predicts that the characteristic variety of a generic polynomial vector field has no homogeneous involutive subvarieties besides the zero section and subvarieties of fibers over singular points.