Absorbing Multiplication Modules Over Pullback Rings

Absorbing Comultiplication Modules Over a Pullback Ring

“…The R-modules of deleted and block cycle types correspond exactly to the G(R)-modules of string and band types (see [8]). Modules over pullback rings have been studied by several authors (see for instance, [2], [7], [10], [12], [14], [15], [16], [17], [19], [20], [21], [23], [24], [25], [26], [29], [38]). Notably, there is the important work of Levy [25], resulting in the classification of all finitely generated indecomposable modules over Dedekind-like rings.…”

On Quasi Comultiplication Modules Over Pullback Rings

“…Then Ker(R →R) = P = P 1 × P 2 , R/P ∼ =R ∼ = R 1 /P 1 ∼ = R 2 /P 2 , and P 1 P 2 = P 2 P 1 = 0 (so R is not a domain). Furthermore, there is an exact sequence 0 → P i → R → R j → 0 of R-modules (see [21]), for i = j. Modules over pullback rings have been studied by several authors (see for example [4], [8], [9], [11], [12], [14], [15], [18], [19], [23] and [28]). Notably, there is the monumental work of Levy [22], resulting in the classification of all finitely generated indecomposable modules over Dedekind-like rings.…”