Abstract. We, in this paper, study the commutativity of skew polynomials at zero as a generalization of an α-rigid ring, introducing the concept of strongly skew reversibility. A ring R is be said to be strongly α-skew reversible if the skew polynomial ring R[x; α] is reversible. We examine some characterizations and extensions of strongly α-skew reversible rings in relation with several ring theoretic properties which have roles in ring theory.

In this paper, the (quasi-)Baerness of skew group ring and fixed ring is investigated. The following two results are obtained: if R is a simple ring with identity and G an outer automorphism group, then R  G is a Baer ring; if R is an Artinian simple ring with identity and G an outer automorphism group, then R G is a Baer ring. Moreover, by decomposing Morita Context ring and Morita Context Theory, we provided several conditions of Morita Context ring, which is formed of skew group ring and fixed ring, to be (quasi-)Baer ring.

In this paper, we introduce a class Ψ of real functions defined on the set of non-negative real numbers, and obtain a new unique common fixed point theorem for four mappings satisfying Ψ-contractive condition on a non-complete 2-metric space and give the versions of the corresponding result for two and three mappings.

Insertion-of-factors-property, which was introduced by Bell, has a role in the study of various sorts of zero-divisors in noncommutative rings. We in this note consider this property in the case that factors are restricted to maximal ideals. A ring is called IMIP when it satisfies such property. It is shown that the Dorroh extension of A by K is an IMIP ring if and only if A is an IFP ring without identity, where A is a nil algebra over a field K. The structure of an IMIP ring is studied in relation to various kinds of rings which have roles in noncommutative ring theory.