On generalizations of soft ideals of rings

In the first chapter of in this thesis, definitions such as group, ring, subring, ideal, radical of an ideal, prime ideal, 1-absorbing prime ideal, which we will use in the following sections, and theorems are given. Plus in this section, starting from the introduction of the theory of soft sets, some definitions and theorems built on soft sets are given. In this section, algebraic properties of soft int-rings and soft int-ideals are examined. On the other hand, ideals have a very crucial role in algebra; since the more we have information about the ideal(s) of a ring, the more information we have information about the ring itself. Ideals are not the only kind, perhaps the most important of these types are prime ideals. Therefore, in this study, the transformation of the concept of soft prime int-ideal to the theory of soft sets and the generalization of soft prime int-ideals have been studied. In the second section, some new definitions such as soft nilpotent element, soft idempodent element, soft zero divisor, soft non-explicit ideal were introduced, and applications of these definitions were also carried out. In addition, several applications of these new definitions were carried out as regards the soft prime int-ideal concept. In the third section, the first generalized form of the soft prime int-ideal concept, soft near prime int-ideal, is introduced and some algebraic properties are examined. In the forth section, the concept of soft 1-absorbing prime int-ideal, which is another generalization of the concept of soft prime int-ideal, is introduced and its some algebraic properties are examined. Some studies related to the fourth chapter are creating a 1-absorbing prime ideal of R owing to soft 1-absorbing prime int-ideal of R and obtaining soft 1-absorbing prime int-ideals of R and R/I with the same characteristics.