Many new results were obtained in this paper about P.P. ring. Semi-primitive ring R with (dcc) on principal-ideal P is always P.P.ring. Also, St-G-P.P. ring R is given to answer new question; is B-rings are P.P. ring. Also regular and Von Neumann regular rings are introduced to find a relationship between P.P. ring and these kind of the rings.
In this paper, we study neutrosophic of one important types of algebra namely BCK-algebra. Some new results of a generalization of BCK-algebra (Ω-BCK-algebra) have been introduced. Several facts about neutrosophic Ω-BCK-algebra are presented such as neutrosophic of homomorphic image and neutrosophic of kernel homomorphism. Finally, some definitions, examples, and other properties of neutrosophic BCK-algebra and neutrosophic Ω-BCK-algebra are given.
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