Stacked Bases Theorems for Finitely Generated Primary Modules over a principal ideal domain
by
Pudji Astuti
Dept. of Math.,Institut Teknologi Bandung, Indonesia
Coauthors: Xavier Puerta (Dept. de Matemàtica Aplicada I, Universitat Politècnica de Catalunya, Spain), Harald K. Wimmer (Mathematisches Institut, Universität Würzburg, Germany)

Let M be a finitely generated primary module over a principal ideal domain R for a prime element p and W subset M be a submodule. A basis of W, i.e. a subset {y₁, ..., y_r} subset W satisfying W = \oplus^r_i=1 < y_i > , is stacked if there exists {u₁, ..., u_k} subset M a basis of M such that y_i = p^h_i u_i, i = 1, ..., r. We prove necessary and sufficent conditions for a basis to be stacked and for a submodule to have a stacked basis. The conditions are derived as a generalization of characterization of extendible Jordan bases and Marked subspaces by Bru et. al. and by Ferrer et. al. which involve the concepts of constancy property, depth property and double filtration submodules.

Date received: December 20, 2000