caa a22 4500 477094791 CHVBK 20180405111524.0 cr unu---uuuuu 170330e19961101xx s 000 0 eng 10.1007/BF03322195 doi (NATIONALLICENCE)springer-10.1007/BF03322195 Classification of Modules with Two Distinguished Pure Submodules and Bounded Quotients [Elektronische Daten] [Manfred Dugas, Rüdiger Göbel] In this paper, we consider modules over principal ideal domains R. The objects are free R- modules F with two distinguished pure submodules F 0 and F1 with F 0 ∩ F1 = 0 and bounded quotient F/(F 0 ⊕ F 1) and morphisms are the usual R-homomorphisms which preserve the distinguished submodules. This category is denoted by cRep2.R and its objects, we say the cR2-modules are denoted by F = (F, F0, F 1). The rank of a cR2-module F is the rank of the free R-module F. We will show that cR2 -@#@ modules are direct sums of indecomposable cR2-modules of rank 1 or 2. The infinite series of indecomposable cR2-modules is well-known and given explicitly after our Main Theorem 1.4. The result was first shown for cR2modules of finite rank in Arnold and Dugas [4], then for countable rank, using heavy machinery due to Hill and Megibben [25] in Files and Göbel [20]. Our proof for arbitrary rank is based on [20] and illustrates the importance of Hill's notion of an axiom-3 family of modules. The Main Theorem is applied to a classification of Butler groups with two critical types. 1 2 Birkhäuser Verlag, Basel, 1996 tame representation type over the ring ℤ nationallicence decompositions nationallicence Butler groups with small typesets nationallicence Dugas Manfred Department of Mathematics, Baylor University, 76798, Waco, Texas, USA aut Göbel Rüdiger Mathematik und Informatik, Universität Essen, Fachbereich 6, 45117, Essen, Germany aut Results in Mathematics Birkhäuser-Verlag 30/3-4(1996-11-01), 264-275 0378-6218 30:3-4<264 1996 30 25 https://doi.org/10.1007/BF03322195 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/BF03322195 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Dugas Manfred Department of Mathematics, Baylor University, 76798, Waco, Texas, USA aut NATIONALLICENCE 700 1- Göbel Rüdiger Mathematik und Informatik, Universität Essen, Fachbereich 6, 45117, Essen, Germany aut NATIONALLICENCE 773 0- Results in Mathematics Birkhäuser-Verlag 30/3-4(1996-11-01), 264-275 0378-6218 30:3-4<264 1996 30 25 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer