Characterization of irreducible polynomials over a special principal ideal ring
Mathematica Bohemica (2023)
- Volume: 148, Issue: 4, page 501-506
- ISSN: 0862-7959
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topBoudine, Brahim. "Characterization of irreducible polynomials over a special principal ideal ring." Mathematica Bohemica 148.4 (2023): 501-506. <http://eudml.org/doc/299473>.
@article{Boudine2023,
abstract = {A commutative ring $R$ with unity is called a special principal ideal ring (SPIR) if it is a non integral principal ideal ring containing only one nonzero prime ideal, its length $e$ is the index of nilpotency of its maximal ideal. In this paper, we show a characterization of irreducible polynomials over a SPIR of length $2$. Then, we give a sufficient condition for a polynomial to be irreducible over a SPIR of any length $e$.},
author = {Boudine, Brahim},
journal = {Mathematica Bohemica},
keywords = {polynomial; irreducibility; commutative principal ideal ring},
language = {eng},
number = {4},
pages = {501-506},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Characterization of irreducible polynomials over a special principal ideal ring},
url = {http://eudml.org/doc/299473},
volume = {148},
year = {2023},
}
TY - JOUR
AU - Boudine, Brahim
TI - Characterization of irreducible polynomials over a special principal ideal ring
JO - Mathematica Bohemica
PY - 2023
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 148
IS - 4
SP - 501
EP - 506
AB - A commutative ring $R$ with unity is called a special principal ideal ring (SPIR) if it is a non integral principal ideal ring containing only one nonzero prime ideal, its length $e$ is the index of nilpotency of its maximal ideal. In this paper, we show a characterization of irreducible polynomials over a SPIR of length $2$. Then, we give a sufficient condition for a polynomial to be irreducible over a SPIR of any length $e$.
LA - eng
KW - polynomial; irreducibility; commutative principal ideal ring
UR - http://eudml.org/doc/299473
ER -
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