Pseudo BCI-algebras with derivations

Lavinia Corina Ciungu

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arXiv · 1902.09895

Pseudo BCI-algebras with derivations

Lavinia Corina Ciungu

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Abstract

In this paper we define two types of implicative derivations on pseudo-BCI algebras, we investigate their properties and we give a characterization of regular implicative derivations of type II. We also define the notion of a $d$-invariant deductive system of a pseudo-BCI algebra $A$ proving that $d$ is a regular derivation of type II if and only if every deductive system on $A$ is $d$-invariant. It is proved that a pseudo-BCI algebra is $p$-semisimple if and only if the only regular derivation of type II is the identity map. Another main result consists of proving that the set of all implicative derivations of a $p$-semisimple pseudo-BCI algebra forms a commutative monoid with respect to function composition. Two types of symmetric derivations on pseudo-BCI algebras are also introduced and it is proved that in the case of $p$-semisimple pseudo-BCI algebras the sets of type II implicative derivations and type II symmetric derivations are equal.

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Lavinia Corina Ciungu. 2019-02-26. Pseudo BCI-algebras with derivations. https://arxiv.org/abs/1902.09895

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