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Application of soft ideals to two new types: the soft primary ideal and the soft 1-absorbing primary ideal
  • Filiz çıtak,
  • IBRAHIM HALIL KANAT
Filiz çıtak
Gaziosmanpasa University

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IBRAHIM HALIL KANAT
Gaziosmanpasa University
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Abstract

In this paper, we introduce two new types of ideals. The first of these is a soft primary ideal, a generalization of the soft prime ideal. We work theoretically and practically in the first part on this new concept. One of the most important results we have achieved is that the concept of a soft primary ideal is a generalization of a soft prime ideal. Namely, a soft prime ideal is a soft primary ideal, but a primary ideal does not need to be a prime ideal. Another important result is that the radical of a soft primary ideal is a soft prime ideal. In addition, with the help of a soft primary ideal, we obtain a primary ideal of the ring under suitable conditions. In the second part, we describe and examine the concept of a soft 1-absorbing primary ideal, a generalization of the soft primary ideal. In this part, we show that every soft primary ideal is a 1-absorbing primary ideal, but the reverse of this situation is not valid. The soft 1-absorbing primary ideal also is a generalization of the soft prime ideal. In this section, we have proved that the radical of the soft 1-absorbing primary ideal is the soft prime ideal. Finally, we determine that algebraic features of soft primary ideal and soft 1-absorbing primary ideal are guarded under ring homomorphisms.