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Injective And Projective Semimodules Over Involutive Semirings, Peter Jipsen, Sara Vanucci
Injective And Projective Semimodules Over Involutive Semirings, Peter Jipsen, Sara Vanucci
Mathematics, Physics, and Computer Science Faculty Articles and Research
We show that the term equivalence between MV-algebras and MV-semirings lifts to involutive residuated lattices and a class of semirings called involutive semirings. The semiring perspective leads to a necessary and sufficient condition for the interval [d,1] to be a subalgebra of an involutive residuated lattice, where d is the dualizing element. We also import some results and techniques of semimodule theory in the study of this class of semirings, generalizing results about injective and projective MV-semimodules. Indeed, we note that the involution plays a crucial role and that the results for MV-semirings are still true for …