# Centers in domains with quadratic growth

Open Mathematics (2005)

- Volume: 3, Issue: 4, page 644-653
- ISSN: 2391-5455

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topAgata Smoktunowicz. "Centers in domains with quadratic growth." Open Mathematics 3.4 (2005): 644-653. <http://eudml.org/doc/268849>.

@article{AgataSmoktunowicz2005,

abstract = {Let F be a field, and let R be a finitely-generated F-algebra, which is a domain with quadratic growth. It is shown that either the center of R is a finitely-generated F-algebra or R satisfies a polynomial identity (is PI) or else R is algebraic over F. Let r ∈ R be not algebraic over F and let C be the centralizer of r. It is shown that either the quotient ring of C is a finitely-generated division algebra of Gelfand-Kirillov dimension 1 or R is PI.},

author = {Agata Smoktunowicz},

journal = {Open Mathematics},

keywords = {16D90; 16P40; 16S80; 16W50},

language = {eng},

number = {4},

pages = {644-653},

title = {Centers in domains with quadratic growth},

url = {http://eudml.org/doc/268849},

volume = {3},

year = {2005},

}

TY - JOUR

AU - Agata Smoktunowicz

TI - Centers in domains with quadratic growth

JO - Open Mathematics

PY - 2005

VL - 3

IS - 4

SP - 644

EP - 653

AB - Let F be a field, and let R be a finitely-generated F-algebra, which is a domain with quadratic growth. It is shown that either the center of R is a finitely-generated F-algebra or R satisfies a polynomial identity (is PI) or else R is algebraic over F. Let r ∈ R be not algebraic over F and let C be the centralizer of r. It is shown that either the quotient ring of C is a finitely-generated division algebra of Gelfand-Kirillov dimension 1 or R is PI.

LA - eng

KW - 16D90; 16P40; 16S80; 16W50

UR - http://eudml.org/doc/268849

ER -

## References

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