In this paper, we prove that if R is an Archimedean reduced ring and satisfy ACC on
annihilators, then R [[x]] is also an Archimedean reduced ring. More generally, we prove that …

By [12], a ring R is left APP if R has the property that “the left annihilator of a principal ideal is
pure as a left ideal”. Equivalently, R is a left APP-ring if R modulo the left annihilator of any …

Let R be a ring,(S,≤) a strictly ordered monoid, and ω: S→ End (R) a monoid
homomorphism. In [18], Mazurek, and Ziembowski investigated when the skew generalized …

The purpose of this paper is to study the behavior of the IN and SA property with respect to
the skew power series and Laurent series extensions. For an α-compatible ring R it is shown …

Let R be a ring,(S,≤) a strictly ordered monoid and ω: S→ End (R) a monoid
homomorphism. In this note for a (S, ω)-Armendariz ring R we study some properties of skew …

In this note we study the structures of power-serieswise Armendariz rings and IFP rings
when they are skewed by ring endomorphisms (or automorphisms). We call such rings skew …

In this note we study the ascending chain conditions on principal left (resp. right) ideals of
the skew polynomial ring Rx;α,δ. We give a characterization of skew polynomial rings Rx;α,δ …

In this paper, we continue to study skew inverse Laurent series ring R ((x− 1; α, δ)), where R
is a ring equipped with an automorphism α and an α-derivation δ. We directly prove that R …

In the present note, we continue the study of skew inverse Laurent series ring R ((x− 1; α, δ))
and skew inverse power series ring R [[x− 1; α, δ]], where R is a ring equipped with an …

Let R be a ring, S a strictly ordered monoid, and ω: S→ End (R) a monoid homomorphism.
In, Marks, Mazurek, and Ziembowski study the (S, ω)-Armendariz condition on R, a …