Study Neutrosophic Quasi-Frobenius by Local and Artinian Rings

Omar A. Khashan^1,*, Majid M. Abed²

¹Department of Mathematics, College of Computer Sciences and Mathematics, University of Tikrit, Tikrit, Iraq

²Department of Mathematics, College of Education for Pure Science, University Of Anbar, Ramadi, Anbar, Iraq

Emails: omar1990@st.tu.edu.iq; majid_math@uoanbar.edu.iq

Abstract

In this paper, we study the relationships between the Neutrosophic quasi-Frobenius rings and the Neutrosophic of local rings and Artinian rings. In addition, we present study the relationship between the Neutrosophic quasi-Frobenius ring and some concepts such as Neutrosophic semisimple ring, Neutrosophic module injective and Neutrosophic Noetherian ring. Finally, we introduce some mathematical formulas with an commutative, coherent and Neutrosophic perfect ring, through which we obtain the Neutrosophic quasi-Frobenius ring.

Keywords: Quasi-Frobenius rings; Artinian rings; Local rings; Noetherian ring