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Autor:
P. V Danchev
Publikováno v:
Известия Иркутского государственного университета: Серия "Математика", Vol 27, Iss 1, Pp 28-35 (2019)
We introduce the notions of left and right cleanness and nil cleanness in rings showing their close relationships with the classical concepts of cleanness and nil cleanness. Specifically, it is proved that strongly clean rings are both L-clean and R-
Externí odkaz:
https://doaj.org/article/a06e92be741b4295a6eff057921d9fb4
Autor:
Peter V. Danchev
Publikováno v:
Journal of Taibah University for Science, Vol 13, Iss 1, Pp 121-123 (2019)
We completely characterize up to an isomorphism those rings whose elements satisfy the equations $ x^4=x $ or $ x^4=-x $ . Specifically, it is proved that a ring is weakly quadratent if, and only if, it is isomorphic to either K, $ \mathbb {Z}_3 $ ,
Externí odkaz:
https://doaj.org/article/02929568c5044c009aff7dce974dbaf2
Publikováno v:
Acta Mathematica Hungarica. 168:186-201
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::c7d49bf8750317cda58c63a2a28ce12f
https://doi.org/10.1007/s10474-022-01262-x
https://doi.org/10.1007/s10474-022-01262-x
Autor:
Peter V. Danchev
Publikováno v:
Ural Mathematical Journal, Vol 5, Iss 1 (2019)
A ring \(R\) is called weakly invo-clean if any its element is the sum or the difference of an involution and an idempotent. For each commutative unital ring \(R\) and each abelian group \(G\), we find only in terms of \(R\), \(G\) and their sections
Externí odkaz:
https://doaj.org/article/d956632194a84ceba95ff097ac41e8bc
Autor:
P. V. Danchev, D. D. Anderson
Publikováno v:
Proceedings of the American Mathematical Society. 148:5087-5089
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::7f53aa94564f40fbf80b4bc1fad27af6
https://doi.org/10.1090/proc/15246
https://doi.org/10.1090/proc/15246
Autor:
P. V. Danchev
Publikováno v:
Lobachevskii Journal of Mathematics. 40:36-41
We classify those rings in which all elements are linear combinations over ℤ of at most three commuting idempotents. Our results improve on recent publications by the author in Albanian J. Math. (2018), Gulf J. Math. (2018), Bull. Iran. Math. Soc.
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::f977302ee23a8afee9ffb74b85b08641
https://doi.org/10.1134/s1995080219010050
https://doi.org/10.1134/s1995080219010050
Autor:
D. D. Anderson, P. V. Danchev
Publikováno v:
Springer Proceedings in Mathematics & Statistics ISBN: 9789811684210
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::49bb748c42fc74e65e4145b3b628ac71
https://doi.org/10.1007/978-981-16-8422-7_13
https://doi.org/10.1007/978-981-16-8422-7_13
Autor:
P. V. Danchev
Publikováno v:
Известия Иркутского государственного университета: Серия "Математика", Vol 31, Iss 1, Pp 150-151 (2020)
The author wish to add the following to the Acknowledgement section of this Article ”The author would like to express his sincere thanks to Dr. Janez Ster from University of Ljubljana for their joint communication on the subject of the paper and va
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::cfb53235311e6b0a226573a889098958
https://doi.org/10.26516/1997-7670.2020.31.150
https://doi.org/10.26516/1997-7670.2020.31.150
Autor:
P. V. Danchev
Publikováno v:
Irish Mathematical Society Bulletin. :9-17
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::b896f6842aadd40978f1af9d78817908
https://doi.org/10.33232/bims.0077.9.17
https://doi.org/10.33232/bims.0077.9.17