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Almost Completely Decomposable Groups and Integral Linear Algebra

✍ Scribed by K Benabdallah; A Mader

Publisher
Elsevier Science
Year
1998
Tongue
English
Weight
351 KB
Volume
204
Category
Article
ISSN
0021-8693

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✦ Synopsis

. where ‫ޚ‬ is the set of all 1 = k integral matrices k-tuples , N is a nonsingular integral k = k matrix, and a w is a k = 1 matrix with entries from A. Here juxtaposition denotes the ordinary matrix and scalar multi-Ž . w plications. Thus adj N a is a k = 1 matrix of certain integral linear w y1 w Ž . Ž . w combinations of the entries of a ; further N a s 1rdet N adj N a is © y1 w a k = 1 matrix of elements in a fixed divisible hull ‫ޑ‬ A of A, and ‫ޚ‬ N a

is the set of all products ␣ N a , where ␣ g ‫,ޚ‬ i.e., the subgroup of ‫ޑ‬ A generated by the entries of N y1 a w . This shows that the representation is well defined. In addition, N and a w may be assumed to be ''relatively

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