Extending a splitting criterion on mixed modules

Classification of mixed modules

“…But here we prefer a representation of modules as extensions of torsion by torsionfree and denote the relations by the method established in [6], since there seems to be the possibility to extend the results to the bigger class of all modules of finite quotient p-rank, cf. [7], using a description of the torsion submodule by a straight basis, introduced by Benabdallah and Honda [1].…”

Characterizing a class of simply presented modules by relation arrays

“…This paper characterizes the simply presented modules in a class of mixed modules h with the property that the torsion submodule is a direct sum of cyclics and the quotient modulo the torsion submodule is divisible of arbitrary rank. This class was described by generators and relations and the concept of a relation array and its properties studied in a series of papers [4,6,7,8]. In [6] we gave a splitting criterion in terms of the relation array which was extended in [7] to a larger class where the quotient p-rank is finite.…”

“…This class was described by generators and relations and the concept of a relation array and its properties studied in a series of papers [4,6,7,8]. In [6] we gave a splitting criterion in terms of the relation array which was extended in [7] to a larger class where the quotient p-rank is finite. In this paper we show the connection between the calculation of indicators done in [4] and the relation arrays.…”