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Abstract
In this paper we consider the problem of characterizing the invariant factors of three matrices A B, and C, such that AB — C Our matrices have entries over a principal ideal domain or over a local domain. In Section 2 we show that this problem is localizablc
The above problem lias a well-known solution in terms of Littlewood-Richardson sequences. We introduce the concept of a matrix realization of a Littlewood-Richardson sequence. The main result is an explicit construction of a sequence of matrices which realizes a previously given Littlewood Richardson sequence. Our methods offer a matrix theoretical proof of a well-known result of T, Klein on extensions of p-modules.
∗Work supported by the Instituto Nacional de Investigação Cientifica.
†Work supported by the Instituto Nacional de Investigação Cientifica and Junta Nacional de Investigação Cientifica.
∗Work supported by the Instituto Nacional de Investigação Cientifica.
†Work supported by the Instituto Nacional de Investigação Cientifica and Junta Nacional de Investigação Cientifica.
Notes
∗Work supported by the Instituto Nacional de Investigação Cientifica.
†Work supported by the Instituto Nacional de Investigação Cientifica and Junta Nacional de Investigação Cientifica.