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Open AccessArticle

Primeness of Relative Annihilators in BCK-Algebra

1
Center for Information Technologies and Applied Mathematics, University of Nova Gorica, Vipavska 13, 5000 Nova Gorica, Slovenia
2
Department of Mathematics, University of Tabuk, Tabuk 71491, Saudi Arabia
*
Author to whom correspondence should be addressed.
Symmetry 2020, 12(2), 286; https://doi.org/10.3390/sym12020286 (registering DOI)
Received: 15 January 2020 / Revised: 10 February 2020 / Accepted: 11 February 2020 / Published: 15 February 2020
Conditions that are necessary for the relative annihilator in lower B C K -semilattices to be a prime ideal are discussed. Given the minimal prime decomposition of an ideal A, a condition for any prime ideal to be one of the minimal prime factors of A is provided. Homomorphic image and pre-image of the minimal prime decomposition of an ideal are considered. Using a semi-prime closure operation “ c l ”, we show that every minimal prime factor of a c l -closed ideal A is also c l -closed.
Keywords: lower BCK-semilattice; relative annihilator; semi-prime closure operation; minimal prime decomposition; minimal prime factor lower BCK-semilattice; relative annihilator; semi-prime closure operation; minimal prime decomposition; minimal prime factor
MDPI and ACS Style

Bordbar, H.; Muhiuddin, G.; Alanazi, A.M. Primeness of Relative Annihilators in BCK-Algebra. Symmetry 2020, 12, 286.

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