Result: A DIVISION ALGORITHM: A division algorithm

Title:
A DIVISION ALGORITHM: A division algorithm
Authors:
Fred Richman
Source:
Journal of Algebra and Its Applications. :441-449
Publisher Information:
World Scientific Pub Co Pte Lt, 2005.
Publication Year:
2005
Subject Terms:
Polynomial rings and ideals, rings of integer-valued polynomials, 0101 mathematics, Intuitionistic mathematics, 01 natural sciences
Document Type:
Academic journal Article
File Description:
application/xml
Language:
English
ISSN:
1793-6829
0219-4988
DOI:
10.1142/s0219498805001289
Access URL:
https://zbmath.org/2226292
https://doi.org/10.1142/s0219498805001289
http://math.fau.edu/richman/Docs/heyting3.pdf
https://www.worldscientific.com/doi/10.1142/S0219498805001289
Accession Number:
edsair.doi.dedup.....1d24ff0ca172e3374499b4aac37f74b3
Database:
OpenAIRE

Further Information

A divisibility test of Arend Heyting, for polynomials over a field in an intuitionistic setting, may be thought of as a kind of division algorithm. We show that such a division algorithm holds for divisibility by polynomials of content 1 over any commutative ring in which nilpotent elements are zero. In addition, for an arbitrary commutative ring R, we characterize those polynomials g such that the R-module endomorphism of R[X] given by multiplication by g has a left inverse.