Akademik Veri Yönetim Sistemi
10TH INTERNATIONAL CONFERENCE ON APPLIED SCIENCES, Kırklareli, Türkiye, 6 - 08 Ocak 2024, ss.54-57
In this study, ideal and regular matrices are discussed. Ideal theory is very important in commutative rings. The new definition of poloid and the concept of ideal on these sets are brought together in this paper. Studies are shown that the concept of poloid is introduced with the addition of the property P4 (A = BP = PC) on the monoid. This concept created new requirements for existing operations on matrices and division ( A
B
). The current studies have
shown that the definition of poloid is necessary. Matrices and multiplication of matrices are the best examples of the concept of poloid. In matrices, every element is not invertible. Therefore, every element is not commutative. The property P4 exhibits the new situation in this respect. The study is about this exact subject. We are combined sets, arithmetic operations and poloid property in this study. The concepts, theorems and properties defined on commutative rings are discussed. The new concepts, theorems, lemmas and properties are given. The case of the property P4, which is similar to the commutative property (BP = PB), on ideals is analyzed, In this study, the new approaches to the concepts of regular matrices and ideals are presented. Ideals are related to algebraic structures. In this respect, ideals are similar to poloids. Thus, this situation helps to compare the structures. The presence or absence of common properties of these two algebraic structures are constituted other aspects of the study. The study is enriched with examples. Some connections of the two ideas are emphasized.