Abstract
Let R be a ring and (S, ≤) a strictly ordered monoid. Properties of the ring [[R S,≤]] of generalized power series with coefficients in R and exponents in S are considered in this paper. It is shown that [[R S,≤]] is reduced (2-primal, Dedekind finite, clean, uniquely clean) if and only if R is reduced (2-primal, Dedekind finite, clean, uniquely clean, respectively) under some additional conditions. Also a necessary and sufficient condition is given for rings under which the ring [[R S,≤]] is a reduced left PP-ring.
Acknowledgments
The author wishes to express his sincere thanks to the referee for his/her valuable suggestions. This work was supported by National Natural Science Foundation of China (10171082) and NWNU-KJCXGC212, TRAPOYT.
Notes
#Communicated by E. Puczylowski.