Cyclic direct summands of modules

An open problem from the list of Eisenbud, cf. [DE] p. 367, connected with Groebner bases algorithm is the computation of the decomposition of module into direct summands. We present an approach to compute all cyclic summands of a module over a local or graded algebra over a field. A cyclic module is generated by one element, i.e. it is a quotient of the algebra itself. The algorithm involves Groebner bases, syzygy computations and solving of a system of polynomial bilinear equations. Because of its high complexity, the practical use is limited to not very complicated cases. Any direct summand of a module induces a cyclic summand of some higher outer product of the module. From the non-existence of cyclic direct summands in all higher outer products of a module we deduce a sufficient condition for its indecomposability. (orig.)SIGLEAvailable from TIB Hannover: RR 7760(1999,9) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekDEGerman