Estimates of global dimension

Wei Jiaqun

Czechoslovak Mathematical Journal (2006)

  • Volume: 56, Issue: 2, page 773-780
  • ISSN: 0011-4642

Abstract

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In this note we show that for a * n -module, in particular, an almost n -tilting module, P over a ring R with A = E n d R P such that P A has finite flat dimension, the upper bound of the global dimension of A can be estimated by the global dimension of R and hence generalize the corresponding results in tilting theory and the ones in the theory of * -modules. As an application, we show that for a finitely generated projective module over a VN regular ring R , the global dimension of its endomorphism ring is not more than the global dimension of R .

How to cite

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Jiaqun, Wei. "Estimates of global dimension." Czechoslovak Mathematical Journal 56.2 (2006): 773-780. <http://eudml.org/doc/31066>.

@article{Jiaqun2006,
abstract = {In this note we show that for a $\ast ^\{n\}$-module, in particular, an almost $n$-tilting module, $P$ over a ring $R$ with $A=\mathop \{\mathrm \{E\}nd\}_\{R\}P$ such that $P_A$ has finite flat dimension, the upper bound of the global dimension of $A$ can be estimated by the global dimension of $R$ and hence generalize the corresponding results in tilting theory and the ones in the theory of $\ast $-modules. As an application, we show that for a finitely generated projective module over a VN regular ring $R$, the global dimension of its endomorphism ring is not more than the global dimension of $R$.},
author = {Jiaqun, Wei},
journal = {Czechoslovak Mathematical Journal},
keywords = {global dimension; $\ast $-module; global dimension; -modules; selforthogonal modules; -modules; tilting modules; star-modules; homological dimensions; selfsmall modules; endomorphism rings; flat dimension},
language = {eng},
number = {2},
pages = {773-780},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Estimates of global dimension},
url = {http://eudml.org/doc/31066},
volume = {56},
year = {2006},
}

TY - JOUR
AU - Jiaqun, Wei
TI - Estimates of global dimension
JO - Czechoslovak Mathematical Journal
PY - 2006
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 56
IS - 2
SP - 773
EP - 780
AB - In this note we show that for a $\ast ^{n}$-module, in particular, an almost $n$-tilting module, $P$ over a ring $R$ with $A=\mathop {\mathrm {E}nd}_{R}P$ such that $P_A$ has finite flat dimension, the upper bound of the global dimension of $A$ can be estimated by the global dimension of $R$ and hence generalize the corresponding results in tilting theory and the ones in the theory of $\ast $-modules. As an application, we show that for a finitely generated projective module over a VN regular ring $R$, the global dimension of its endomorphism ring is not more than the global dimension of $R$.
LA - eng
KW - global dimension; $\ast $-module; global dimension; -modules; selforthogonal modules; -modules; tilting modules; star-modules; homological dimensions; selfsmall modules; endomorphism rings; flat dimension
UR - http://eudml.org/doc/31066
ER -

References

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