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Minimal polynomials and characteristic polynomials over rings
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Description
type:text
Let R be a commutative ring with 1, and M be a free module of a finite rank over R. is the endomorphism ring of M over R, s is an element in and the matrix of s diagonalizable. Our purpose is to investigate the relationship between the characteristic polynomial of s and the minimal polynomial of s. If R is an integral domain, then we shall show that is uniquely determined as a monic polynomial dividing Also, the difference between the two sets of zeros of and respectively, is only the multiplicity of their roots. If R is not an integral domain, then we shall construct s such that is not necessarily monic nor divides
identifier:JOS-09725555-2001
Journal
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- JP journal of algebra, number theory and applications
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JP journal of algebra, number theory and applications 20 (1), 49-60, 2011-03
Pushpa Publishing House
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Keywords
Details 詳細情報について
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- CRID
- 1050282677766391808
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- NII Article ID
- 120005518474
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- NII Book ID
- AA12017469
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- ISSN
- 09725555
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- Text Lang
- en
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- Article Type
- journal article
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- Data Source
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- IRDB
- CiNii Articles