On p -injectivity, YJ-injectivity and quasi-Frobeniusean rings

Roger Yue Chi Ming

Commentationes Mathematicae Universitatis Carolinae (2002)

  • Volume: 43, Issue: 1, page 33-42
  • ISSN: 0010-2628

Abstract

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A new characteristic property of von Neumann regular rings is proposed in terms of annihilators of elements. An ELT fully idempotent ring is a regular ring whose simple left (or right) modules are either injective or projective. Artinian rings are characterized in terms of Noetherian rings. Strongly regular rings and rings whose two-sided ideals are generated by central idempotents are characterized in terms of special annihilators. Quasi-Frobeniusean rings are characterized in terms of p -injectivity. Also, a commutative YJ-injective ring with maximum condition on annihilators and finitely generated socle is quasi-Frobeniusean.

How to cite

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Yue Chi Ming, Roger. "On $p$-injectivity, YJ-injectivity and quasi-Frobeniusean rings." Commentationes Mathematicae Universitatis Carolinae 43.1 (2002): 33-42. <http://eudml.org/doc/248996>.

@article{YueChiMing2002,
abstract = {A new characteristic property of von Neumann regular rings is proposed in terms of annihilators of elements. An ELT fully idempotent ring is a regular ring whose simple left (or right) modules are either injective or projective. Artinian rings are characterized in terms of Noetherian rings. Strongly regular rings and rings whose two-sided ideals are generated by central idempotents are characterized in terms of special annihilators. Quasi-Frobeniusean rings are characterized in terms of $p$-injectivity. Also, a commutative YJ-injective ring with maximum condition on annihilators and finitely generated socle is quasi-Frobeniusean.},
author = {Yue Chi Ming, Roger},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {von Neumann regular; $V$-ring; Artinian ring; $p$-injectivity; YJ-injectivity; quasi-Frobeniusean; von Neumann regular rings; -rings; Artinian rings; YJ-injectivity; quasi-Frobenius rings; annihilator conditions},
language = {eng},
number = {1},
pages = {33-42},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {On $p$-injectivity, YJ-injectivity and quasi-Frobeniusean rings},
url = {http://eudml.org/doc/248996},
volume = {43},
year = {2002},
}

TY - JOUR
AU - Yue Chi Ming, Roger
TI - On $p$-injectivity, YJ-injectivity and quasi-Frobeniusean rings
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2002
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 43
IS - 1
SP - 33
EP - 42
AB - A new characteristic property of von Neumann regular rings is proposed in terms of annihilators of elements. An ELT fully idempotent ring is a regular ring whose simple left (or right) modules are either injective or projective. Artinian rings are characterized in terms of Noetherian rings. Strongly regular rings and rings whose two-sided ideals are generated by central idempotents are characterized in terms of special annihilators. Quasi-Frobeniusean rings are characterized in terms of $p$-injectivity. Also, a commutative YJ-injective ring with maximum condition on annihilators and finitely generated socle is quasi-Frobeniusean.
LA - eng
KW - von Neumann regular; $V$-ring; Artinian ring; $p$-injectivity; YJ-injectivity; quasi-Frobeniusean; von Neumann regular rings; -rings; Artinian rings; YJ-injectivity; quasi-Frobenius rings; annihilator conditions
UR - http://eudml.org/doc/248996
ER -

References

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