A short note on categorical equivalences of proper weak pseudo EMV-algebras

Document Type : Original Article

Author

1 Mathematical Institute, Slovak Academy of Sciences, Stef´anikova 49, SK-814 73 Bratislava, Slovakia ˇ

2 Palack´y University Olomouc, Faculty of Sciences, tˇr. 17. listopadu 12, CZ-771 46 Olomouc, Czech Republi

Abstract

We study the class of weak pseudo EMV-algebras without top element that are a non-commutative generalization of MV-algebras, pseudo MV-algebras and generalized Boolean algebras. We present their categorical equivalences to a special category of pseudo MV-algebras with a fixed maximal and normal ideal as well as to a special category of unital l-groups with a fixed maximal and normal l-ideal.

Keywords