Idempotents and the multiplicative group of some totally bounded rings

Mohamed A. Salim; Adela Tripe

Czechoslovak Mathematical Journal (2011)

  • Volume: 61, Issue: 2, page 509-519
  • ISSN: 0011-4642

Abstract

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In this paper, we extend some results of D. Dolzan on finite rings to profinite rings, a complete classification of profinite commutative rings with a monothetic group of units is given. We also prove the metrizability of commutative profinite rings with monothetic group of units and without nonzero Boolean ideals. Using a property of Mersenne numbers, we construct a family of power 2 ℵ 0 commutative non-isomorphic profinite semiprimitive rings with monothetic group of units.

How to cite

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Salim, Mohamed A., and Tripe, Adela. "Idempotents and the multiplicative group of some totally bounded rings." Czechoslovak Mathematical Journal 61.2 (2011): 509-519. <http://eudml.org/doc/196811>.

@article{Salim2011,
abstract = {In this paper, we extend some results of D. Dolzan on finite rings to profinite rings, a complete classification of profinite commutative rings with a monothetic group of units is given. We also prove the metrizability of commutative profinite rings with monothetic group of units and without nonzero Boolean ideals. Using a property of Mersenne numbers, we construct a family of power $2^\{\aleph _0\}$ commutative non-isomorphic profinite semiprimitive rings with monothetic group of units.},
author = {Salim, Mohamed A., Tripe, Adela},
journal = {Czechoslovak Mathematical Journal},
keywords = {compact ring; group of units; Jacobson radical; left linearly compact ring; Mersenne number; monothetic group; primary ring; summable set; totally bounded ring; linearly compact rings; groups of units; Jacobson radical; Mersenne numbers; monothetic groups; primary rings; summable sets; totally bounded rings; profinite commutative rings; metrizability},
language = {eng},
number = {2},
pages = {509-519},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Idempotents and the multiplicative group of some totally bounded rings},
url = {http://eudml.org/doc/196811},
volume = {61},
year = {2011},
}

TY - JOUR
AU - Salim, Mohamed A.
AU - Tripe, Adela
TI - Idempotents and the multiplicative group of some totally bounded rings
JO - Czechoslovak Mathematical Journal
PY - 2011
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 61
IS - 2
SP - 509
EP - 519
AB - In this paper, we extend some results of D. Dolzan on finite rings to profinite rings, a complete classification of profinite commutative rings with a monothetic group of units is given. We also prove the metrizability of commutative profinite rings with monothetic group of units and without nonzero Boolean ideals. Using a property of Mersenne numbers, we construct a family of power $2^{\aleph _0}$ commutative non-isomorphic profinite semiprimitive rings with monothetic group of units.
LA - eng
KW - compact ring; group of units; Jacobson radical; left linearly compact ring; Mersenne number; monothetic group; primary ring; summable set; totally bounded ring; linearly compact rings; groups of units; Jacobson radical; Mersenne numbers; monothetic groups; primary rings; summable sets; totally bounded rings; profinite commutative rings; metrizability
UR - http://eudml.org/doc/196811
ER -

References

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