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On the rational relationships among pseudo-roots of a non-commutative polynomial
- Source :
- Journal of Pure and Applied Algebra. 225:106581
- Publication Year :
- 2021
- Publisher :
- Elsevier BV, 2021.
-
Abstract
- For a non-commutative ring R, we consider factorizations of polynomials in R[t] where t is a central variable. A pseudo-root of a polynomial p(t) is an element x in R, for which there exist polynomials q(t) and s(t) such that p(t)=q(t)(t-x)s(t). We investigate the rational relationships that hold among the pseudo-roots of p(t) by using the diamond operations for cover graphs of modular lattices.<br />Minor corrections, to appear in "Journal of Pure and Applied Algebra"
- Subjects :
- Polynomial
Algebra and Number Theory
Graph theoretic
010102 general mathematics
Mathematics - Rings and Algebras
01 natural sciences
Combinatorics
Rings and Algebras (math.RA)
Lattice (order)
0103 physical sciences
FOS: Mathematics
Division ring
Greatest common divisor
Mathematics - Combinatorics
16K99 (Primary) 06C99 (Secondary)
Combinatorics (math.CO)
010307 mathematical physics
0101 mathematics
Commutative property
Monic polynomial
Least common multiple
Mathematics
Subjects
Details
- ISSN :
- 00224049
- Volume :
- 225
- Database :
- OpenAIRE
- Journal :
- Journal of Pure and Applied Algebra
- Accession number :
- edsair.doi.dedup.....40ed097b13bee6a84999eca9b01ccf51