we introduce the notion ofstrongly $alpha$-reversible rings which is a strong version of$alpha$-reversible rings, and investigate its properties. we firstgive an example to show that strongly reversible rings need not bestrongly $alpha$-reversible. we next argue about the strong$alpha$-reversibility of some kinds of extensions. a number ofproperties of this version are established. it is shown ...

A skew generalized power series ring R[[S, ω]] consists of all functions from a strictly ordered monoid S to a ring R whose support contains neither infinite descending chains nor infinite antichains, with pointwise addition, and with multiplication given by convolution twisted by an action ω of the monoid S on the ring R. Special cases of the skew generalized power series ring construction are...

In this note, we introduce the concept of semi-*-IFP, involutive version semi-IFP, which is a generalization quasi-*-IFP and *-reducedness *-rings. We study basic structure properties *-rings having semi-*-IFP give results for IFPs in rings with involution. Several counterexamples are stated to connect versions IFP. discuss conditions be extended into *-subrings ring upper triangular matrices. ...