Yiarayong Pairote, Wachirawongsakorn Piyada
Department of Mathematics, Faculty of Science and Technology, Pibulsongkram Rajabhat University, Phitsanulok 65000, Thailand.
Faculty of Science and Technology, Pibulsongkram Rajabhat University, Phitsanulok 65000, Thailand.
Heliyon. 2018 Oct 17;4(10):e00863. doi: 10.1016/j.heliyon.2018.e00863. eCollection 2018 Oct.
In this paper we introduce the notion of -algebras as a generalization of -algebras, we investigate its elementary properties. The aim of this paper is to investigate the concept of filters, left ideals (right ideal, ideal) and fuzzy filters in -algebras. Moreover, we investigate relationships between left ideals and filters in -algebras. Furthermore, we characterize filters in terms of fuzzy filters. It is shown that if be a left ideal of a -algebra , then is a left ideal of for all .
在本文中，我们引入了 - 代数的概念作为 - 代数的推广，并研究了其基本性质。本文的目的是研究 - 代数中的滤子、左理想（右理想、理想）和模糊滤子的概念。此外，我们研究了 - 代数中左理想与滤子之间的关系。进一步地，我们用模糊滤子来刻画滤子。结果表明，如果 是 - 代数 的一个左理想，那么对于所有的 ， 是 的一个左理想。
