Tripotents: a class of strongly clean elements in rings

Grigore Călugăreanu

doi:10.2478/auom-2018-0003

.blurhash-client-img { display: none !important; }

Tripotents: a class of strongly clean elements in rings

Analele ştiinţifice ale Universităţii "Ovidius" Constanţa. Seria Matematică

Volume 26 (2018): Issue 1 (March 2018)

By: Grigore Călugăreanu

Open Access

|Mar 2018

Abstract

Periodic elements in a ring generate special classes of strongly clean elements. In particular, elements b such that b = b3+, which are called tripotents and include idempotents, negative of idempotents and order 2 units, are strongly clean. Such elements are determined in 2×2 matrix rings over commutative domains or over arbitrary division rings and for rings of integers modulo n.

References

[1] H. E. Bell A commutativity study for periodic rings. Pacific J. of Math. 70 (1) (1977), 29-36.10.2140/pjm.1977.70.29
Search in Google Scholar Back to article
[2] H. E. Bell, A. Yaqub On generalized periodic-like rings. International J. of Math. and Math. Sciences. Volume 2007, 5 pages.10.1155/2007/29513
Open DOI Search in Google Scholar Back to article
[3] A.M. Bikchentaev, R.S. Yakushev Representation of tripotents and repre- sentations via tripotents. Linear Algebra and its Applications 435 (2011) 2156-2165.10.1016/j.laa.2011.04.003
Search in Google Scholar Back to article
[4] H. Chen On 2 × 2 strongly clean matrices. Bull. Korean Math. Soc. 50 (1) (2013), 125–134.10.4134/BKMS.2013.50.1.125
Open DOI Search in Google Scholar Back to article
[5] A. J. Diesl, T. J. Dorsey Strongly clean matrices over arbitrary rings. Journal of Algebra 399 (2014), 854-869.10.1016/j.jalgebra.2013.08.044
Search in Google Scholar Back to article
[6] L. Fuchs In_nite Abelian Groups. Vol. 2, Academic Press 1973.
Search in Google Scholar Back to article
[7] Y. Hirano and H. Tominaga Rings in which every element is the sum of two idempotents. Bull. Austral. Math. Soc. 37 (2) (1988), 161-164.10.1017/S000497270002668X
Open DOI Search in Google Scholar Back to article
[8] D. Khurana, G. Marks, A. K. Srivastava On unit-central rings. Trends in Math., Springer, Advances in Ring Theory, 205-212.10.1007/978-3-0346-0286-0_13
Search in Google Scholar Back to article
[9] T. Y. Lam A first course in noncommutative rings. Second Edition, GMT 131, Springer Verlag, 2001.10.1007/978-1-4419-8616-0
Search in Google Scholar Back to article

Articles in this issue

DOI: https://doi.org/10.2478/auom-2018-0003 | Journal eISSN: 1844-0835 | Journal ISSN: 1224-1784

Journal RSS Feed

Language: English

Page range: 69 - 80

Submitted on: May 13, 2017

Accepted on: Jun 22, 2017

Published on: Mar 31, 2018

Published by: Ovidius University of Constanta

In partnership with: Paradigm Publishing Services

Publication frequency: 3 issues per year

Keywords:

periodic element,

tripotent,

strongly clean element,

order two unit

Related subjects:

Mathematics,

General mathematics

© 2018 Grigore Călugăreanu, published by Ovidius University of Constanta
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Volume 26 (2018): Issue 1 (March 2018)