关键词: 弱零化子,  , 弱相伴素理想, (α, δ) -相容环

Abstract:

As a generalization of annihilator and associated primes, in this paper, the author introduces the notions of weak annihilator and weak associated primes, and investigates the relationship between the weak associated primes of a ring R and those  of the Ore extension ring R[x; α, δ]. It is proved that if R is an (α, δ)-compatible reversible ring, then N Ass(R[x; α, δ])=P[x; α, δ]| P∈N Ass(R), where N Ass}(R[x; α, δ]) and N Ass}(R) stand for the set of all weak associated primes over R[x; α, δ] and that over R, respectively. So all associated primes over R[x; α, δ] can be described  in terms of the weak associated primes over R in a very straightforward way. Consequently, several results in [3], [5], [6] are generalized to a more general setting.

Key words: Weak annihilator, Weak associated primes, (α, δ)-compatible ring