Some Results on UP-algebras

Subject Areas : Statistics

Zahra Parvizi ¹ (Department of Mathematics, Shahrekord Branch, Islamic Azad University, Shahrekord, Iran)
Somayeh Motamed ² (Department of Mathematics, Bandar Abbas Branch, Islamic Azad University, Bandar Abbas, Iran)
Farhad Khaksar Haghani ³ (Department of Mathematics, Shahrekord Branch, Islamic Azad University, Shahrekord, Iran.)
Javad Moghaderi ⁴ (Department of Mathematics, University of Hormozgan, Bandar Abbas, Iran)

Received: 2020-11-30 Accepted : 2021-04-27 Published : 2022-10-23

Keywords: UP-جبر, پایدارساز, UP-فیلتر, هم‌اتم (قوی), هم‌پوچ‌ساز (توسعه‌یافته),

Abstract :

In this paper, we introduce the concept of stabilizers of a set in UP-algebras and introduce a new class of UP-algebras. Then we introduce and study their properties and the relationships between the left and right stabilizers of a set in UP-algebras and provide equivalent conditions for easier and faster study of new UP-algebras. We also show that, by adding a condition, the left stabilizer of a set is a UP-filter, while the right stabilizer of a set is not. In the following, we define the concepts of coatom and strong coatom on UP-algebras and examine its properties. In addition, we provide equivalent conditions for easier study of coatoms in UP-algebras.We show that for a UP-algebra A, Coatom (A)=A- {0} if and only if each subset of A contains 0, is a UP-filter of A. We also examine the relationship between coatoms and stabilizers. Finally, we introduce the generalized co-annihilator set G relative to F and study its properties.

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