Coprimely packed rings

Tilting modules over almost perfect domains

“…, [21]) An ideal I of a commutative ring R is said to be coprimely packed (resp. compactly packed ), iff for any set of maximal (resp.…”

“…APD's) are coprimely packed if and only if they are compactly packed. By[41] a Dedekind domain is compactly packed (equivalently coprimely packed) if and only if its ideal class group is torsion (see also[21, Theorem 1.4]). Semilocal rings are obviously coprimely packed (by the Prime Avoidance Theorem).…”

On coprimely structured rings

“…Moreover, they showed that if a Noetherian ring R is compactly packed, then dim(R) ≤ 1. After this, Erdogdu generalized the concept of compactly packed rings to coprimely packed rings and investigated the properties of such rings in his paper entitled "Coprimely Packed Rings" [4]. Gilmer formed the dual notion of compactly packed rings in his paper "An Intersection Condition for Prime Ideals" and studied some properties of this notion [6].…”

On the union of graded prime ideals

“…An ideal I is coprimely packed if for an index set ∆ and α ∈ ∆, I + Pα = R implies I α∈∆ Pα where {Pα} α∈∆ is a family of prime ideals of R. If every ideal of R is coprimely packed, then R is a coprimely packed ring. For the studies about coprimely packed rings the reader is referred to [8][9][10]. Finally we show that every graded compactly packed ring is a graded coprimely ring.…”

“…In Section 4, we de ne graded coprimely packed rings that Erdoğdu [8] de ned coprimely packed rings as a generalization of compactly packed rings. An ideal I is coprimely packed if for an index set ∆ and α ∈ ∆, I + Pα = R implies I α∈∆ Pα where {Pα} α∈∆ is a family of prime ideals of R. If every ideal of R is coprimely packed, then R is a coprimely packed ring.…”