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Local pseudo-BCK algebras with pseudo-product

In: Mathematica Slovaca, vol. 61, no. 2
Lavinia Corina Ciungu

Details:

Year, pages: 2011, 127 - 154
Keywords:
pseudo-BCK algebra, deductive system, local pseudo-BCK(pP) algebra, good pseudo-BCK(pP) algebra, maximal deductive system, normal deductive system, primary deductive system, perfect pseudo-BCK(pP) algebra, radical
About article:
Pseudo-BCK algebras were introduced by G. Georgescu and A. Iorgulescu as a generalization of BCK algebras in order to give a corresponding structure to pseudo-MV algebras, since the bounded commutative BCK algebras correspond to MV algebras. Properties of pseudo-BCK algebras and their connections with other fuzzy structures were established by A. Iorgulescu and J. Kühr. The aim of this paper is to define and study the local pseudo-BCK algebras with pseudo-product. We will also introduce the notion of perfect pseudo-BCK algebras with pseudo-product and we will study their properties. We define the radical of a bounded pseudo-BCK algebra with pseudo-product and we prove that it is a normal deductive system. Another result consists of proving that every strongly simple pseudo-hoop is a local bounded pseudo-BCK algebra with pseudo-product.
How to cite:
ISO 690:
Ciungu, L. 2011. Local pseudo-BCK algebras with pseudo-product. In Mathematica Slovaca, vol. 61, no.2, pp. 127-154. 0139-9918. DOI: https://doi.org/10.2478/s12175-011-0001-x

APA:
Ciungu, L. (2011). Local pseudo-BCK algebras with pseudo-product. Mathematica Slovaca, 61(2), 127-154. 0139-9918. DOI: https://doi.org/10.2478/s12175-011-0001-x
About edition: