JP Journal of Algebra, Number Theory and Applications
Volume 29, Issue 1, Pages 17 - 29
(May 2013)
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FACTORIZATION OF AUTOMORPHISMS OF A MODULE OVER A LOCAL RING
Hiroyuki Ishibashi
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Abstract: Let Rbe a commutative local ring with the identity 1 and the unique maximal ideal M be a free module of rank nover R, and s be in
Then, we factorize Minto a direct sum of mfree submodules such that each is s-invariant modulo for and mis the number of the polynomials in the system of invariants of smodulo
Further it is shown that there exists a basis Xfor Mover Rfor which sis factorized into a product of elements in in the form of
where each is a cyclic permutation on X, each is simple, i.e., fixes elements in X. If 2 is a unit in R, then can be replaced by a product of symmetries in As a result if 2 is a unit in R, then sis a product of nor less than nsimple elements. |
Keywords and phrases: minimal polynomial, characteristic polynomial, endomorphisms ring of modules, classical groups. |
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