Some Ring Structures of Skew Genaralized Power Series Rings

Prachi Juyal (Graphic Era (Deemed to be University), Dehradun, Uttrakhand, India)
Satyajeet Singh (Graphic Era (Deemed to be University), Dehradun, Uttrakhand, India)
Seema Saini (Graphic Era (Deemed to be University), Dehradun, Uttrakhand, India)

Journal of the Indonesian Mathematical Society
VOLUME 28 NUMBER 3 (NOVEMBER 2022)

In the current article, we are going to investigate a relationship between some abstract ring structures (weakly PP-rings, clean rings, uniquely clean rings and n-clean rings) along with the skew generalized power series rings A[[N, ϑ]], where A is one of the ring structures described above, (N, ≤) represents a strictly ordered monoid while ϑ : N → End(A) represents a monoid homomorphism. We shall propose unified extensions of the above-mentioned ring structures by employing specific conditions along with their proofs.