Event and Its Application in Algebraic Structures

Young Bae Jun (), Seok-Zun Song and Seon Jeong Kim ()
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Young Bae Jun: Department of Mathematics Education, College of Education, Gyeongsang National University, Jinju 52828, South Korea
Seok-Zun Song: #x2020;Department of Mathematics, Jeju National University, Jeju 63243, South Korea
Seon Jeong Kim: #x2021;Department of Mathematics, Natural Science of College, Gyeongsang National University, Jinju 52828, South Korea

New Mathematics and Natural Computation (NMNC), 2020, vol. 16, issue 01, 105-121

Abstract: The notion of eventful element and eventful set is introduced, and its application is considered in BCI and/or BCK algebras. Several properties are investigated, and (positive implicative) ideal in an eventful BCK algebra and closed ideal in an eventful BCI algebra are discussed. Given the subsets A and B of a BCI and/or BCK algebra, the eventful subset E(A,B) which consists of BCI and/or BCK events with a condition is established. Conditions for the eventful subset E(A,B) to be a (positive implicative) ideal of an eventful BCK algebra are provided, and conditions for the eventful subset E(A,B) to be a (closed) ideal of an event BCI algebra are given. An example to show that the set {0̃} is not a positive implicative ideal in an eventful BCK algebra is provided, and then the conditions for the set {0̃} to be a positive implicative ideal in an eventful BCK algebra are considered.

Keywords: Eventful element; eventful set; BCI event; BCK event; eventful BCI algebra; eventful BCK algebra (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1142/S1793005720500076

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