SPECIAL WEAK PROPERTIES OF GENERALIZED POWER SERIES RINGS Ouyang, Lunqun;
Let be a ring and the set of all nilpotent elements of . For a subset of a ring , we define for all }, which is called a weak annihilator of in . ring is called weak zip provided that for any subset of , if , then there exists a finite subset such that , and a ring is called weak symmetric if for all a, b, . It is shown that a generalized power series ring is weak zip (resp. weak symmetric) if and only if is weak zip (resp. weak symmetric) under some additional conditions. Also we describe all weak associated primes of the generalized power series ring in terms of all weak associated primes of in a very straightforward way.
weak annihilator;weak associated prime;generalized power series;