Very true pseudo-BCK algebras
Lavinia Corina Ciungu

TL;DR
This paper introduces and studies very true operators on pseudo-BCK algebras, exploring their properties, related algebraic structures, and applications to various classes including Smarandache pseudo-BCK algebras.
Contribution
It defines very true operators, investigates their properties, and extends the concept to various algebraic structures and classes, including quotient and Smarandache pseudo-BCK algebras.
Findings
Composition of very true operators commutes iff they are compatible.
Defined pseudo-BCK_{vt,st} algebra with truth-depressing hedges.
Analyzed properties on classes like pseudo-BCK(pP), FL_w, and pseudo-MTL.
Abstract
In this paper we introduce the very true operators on pseudo-BCK algebras and we study their properties. We prove that the composition of two very true operators is a very true operator if and only if they commute. Moreover, given a very true bounded pseudo-BCK algebra , we define the pseudo-BCK algebra by adding two truth-depressing hedges operators associated with . We also define the very true deductive systems and the very true homomorphisms and we investigate their properties. Also, given a normal -deductive system of a very true pseudo-BCK algebra we construct a very true operator on the quotient pseudo-BCK algebra . We investigate the very true operators on some classes of pseudo-BCK algebras such as pseudo-BCK(pP) algebras, FL-algebras, pseudo-MTL algebras. Finally, we define the -Smarandache pseudo-BCK algebras and we introduce the…
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