On McCoy condition and semicommutative rings

Mohamed Louzari

Commentationes Mathematicae Universitatis Carolinae (2013)

  • Volume: 54, Issue: 3, page 329-337
  • ISSN: 0010-2628

Abstract

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Let R be a ring and σ an endomorphism of R . We give a generalization of McCoy’s Theorem [ Annihilators in polynomial rings, Amer. Math. Monthly 64 (1957), 28–29] to the setting of skew polynomial rings of the form R [ x ; σ ] . As a consequence, we will show some results on semicommutative and σ -skew McCoy rings. Also, several relations among McCoyness, Nagata extensions and Armendariz rings and modules are studied.

How to cite

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Louzari, Mohamed. "On McCoy condition and semicommutative rings." Commentationes Mathematicae Universitatis Carolinae 54.3 (2013): 329-337. <http://eudml.org/doc/260747>.

@article{Louzari2013,
abstract = {Let $R$ be a ring and $\sigma $ an endomorphism of $R$. We give a generalization of McCoy’s Theorem [ Annihilators in polynomial rings, Amer. Math. Monthly 64 (1957), 28–29] to the setting of skew polynomial rings of the form $R[x;\sigma ]$. As a consequence, we will show some results on semicommutative and $\sigma $-skew McCoy rings. Also, several relations among McCoyness, Nagata extensions and Armendariz rings and modules are studied.},
author = {Louzari, Mohamed},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {Armendariz rings; McCoy rings; Nagata extension; semicommutative rings; $\sigma $-skew McCoy; Armendariz rings; skew McCoy rings; Nagata extensions; semicommutative rings; right annihilators; skew polynomial rings},
language = {eng},
number = {3},
pages = {329-337},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {On McCoy condition and semicommutative rings},
url = {http://eudml.org/doc/260747},
volume = {54},
year = {2013},
}

TY - JOUR
AU - Louzari, Mohamed
TI - On McCoy condition and semicommutative rings
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2013
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 54
IS - 3
SP - 329
EP - 337
AB - Let $R$ be a ring and $\sigma $ an endomorphism of $R$. We give a generalization of McCoy’s Theorem [ Annihilators in polynomial rings, Amer. Math. Monthly 64 (1957), 28–29] to the setting of skew polynomial rings of the form $R[x;\sigma ]$. As a consequence, we will show some results on semicommutative and $\sigma $-skew McCoy rings. Also, several relations among McCoyness, Nagata extensions and Armendariz rings and modules are studied.
LA - eng
KW - Armendariz rings; McCoy rings; Nagata extension; semicommutative rings; $\sigma $-skew McCoy; Armendariz rings; skew McCoy rings; Nagata extensions; semicommutative rings; right annihilators; skew polynomial rings
UR - http://eudml.org/doc/260747
ER -

References

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