Some Results on UP-algebras
Subject Areas : StatisticsZahra Parvizi 1 , Somayeh Motamed 2 , Farhad Khaksar Haghani 3 , Javad Moghaderi 4
1 - Department of Mathematics, Shahrekord Branch, Islamic Azad University, Shahrekord, Iran
2 - Department of Mathematics, Bandar Abbas Branch, Islamic Azad University, Bandar Abbas, Iran
3 - Department of Mathematics, Shahrekord Branch, Islamic Azad University, Shahrekord,
Iran.
4 - Department of Mathematics, University of Hormozgan, Bandar Abbas, Iran
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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