Abstract
In the present paper, skewed reflexivity with maximal ideal axes by ring endomorphisms has been studied, introducing the concept of an α-skew RM rings, where α is an endomorphism of a given ring to extend the concept of an RM ring and that of an α-rigid ring. First some basic properties of an α-skew RM ring including some examples needed in the process have been considered. Then the characterization of a right α-skew RM ring and their related properties including the trivial extension and Dorroh extension have been investigated . In particular it is shown that for an endomorphism α and n ≥ 2 of a ring R. If R satisfies the condition “aM bRbR = 0 implies aM b = 0 ”and R is a right α-skew RM ring, then Vn(R) is right α¯-skew RM ring. Also the concept of an α-skew RMI ring has been observed . First some basic properties of α-skew RMI rings have been considered. Next α-skew RMI property of some kind of polynomial rings has been investigated.
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