Zobrazeno 1 - 10
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pro vyhledávání: '"Alexander J. Diesl"'
Autor:
Alexander J. Diesl, Alexi Block Gorman
Publikováno v:
Communications in Algebra. 49:4788-4799
A ring is called nil clean if every element can be written as the sum of an idempotent and a nilpotent. The class of nil clean rings has emerged as an important variant of the much-studied class of...
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::70cfafc3725363e298e74fd192bd76f4
https://doi.org/10.1080/00927872.2021.1929276
https://doi.org/10.1080/00927872.2021.1929276
Autor:
Alexander J. Diesl, Daniel R. Shifflet
Publikováno v:
Communications in Algebra. 46:4448-4462
It is unknown whether a power series ring over a strongly clean ring is, itself, always strongly clean. Although a number of authors have shown that the above statement is true in certain special cases, the problem remains open, in general. In this a
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::258ff3291dc15bbbe4fee96de3a88dfc
https://doi.org/10.1080/00927872.2018.1444174
https://doi.org/10.1080/00927872.2018.1444174
Publikováno v:
Communications in Algebra. 46:4131-4147
In this article we investigate the annihilating-ideal graph of a commutative ring, introduced by Behboodi and Rakeei in [10]. Our main goal is to determine which algebraic properties of a ring are ...
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::db675326947bb59761add08535f03192
https://doi.org/10.1080/00927872.2018.1439040
https://doi.org/10.1080/00927872.2018.1439040
Autor:
Wolf Iberkleid, Warren Wm. McGovern, Ramiro Lafuente-Rodriguez, Thomas J. Dorsey, Alexander J. Diesl
Publikováno v:
Journal of Pure and Applied Algebra. 219:4889-4906
We investigate the problem of determining when a triangular matrix ring over a strongly clean ring is, itself, strongly clean. We prove that, if R is a commutative clean ring, then T n ( R ) is strongly clean for every positive n. In the more general
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::cd50bf40cb46d87d5e55da3848f346c3
https://doi.org/10.1016/j.jpaa.2015.03.011
https://doi.org/10.1016/j.jpaa.2015.03.011
Publikováno v:
Journal of Pure and Applied Algebra. 218:661-665
Many authors have investigated the behavior of strong cleanness under certain ring extensions. In this note, we investigate the classical problem of lifting idempotents, in order to consolidate and extend these results. Our main result is that if R i
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::b541f0136544a9afc1e8980d5397cd5e
https://doi.org/10.1016/j.jpaa.2013.08.006
https://doi.org/10.1016/j.jpaa.2013.08.006
Autor:
Thomas J. Dorsey, Alexander J. Diesl
Publikováno v:
Journal of Algebra. 399:854-869
We characterize when the companion matrix of a monic polynomial over an arbitrary ring R is strongly clean, in terms of a type of ideal-theoretic factorization (which we call an iSRC factorization) in the polynomial ring R [ t ] . This provides a non
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::cb64486f5c67d65ab46c832907dfc69e
https://doi.org/10.1016/j.jalgebra.2013.08.044
https://doi.org/10.1016/j.jalgebra.2013.08.044
Autor:
Alexander J. Diesl
Publikováno v:
Journal of Algebra. 383:197-211
Many variations of the notions of clean and strongly clean have been studied by a variety of authors. We develop a general theory, based on idempotents and direct sum decompositions, that unifies several of these existing concepts. As a specific case
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::b0db259af3db03edc0b7c0029059b054
https://doi.org/10.1016/j.jalgebra.2013.02.020
https://doi.org/10.1016/j.jalgebra.2013.02.020
Publikováno v:
Journal of Algebra. 379:208-222
We construct examples of Ore rings satisfying some standard ring-theoretic properties for which the classical rings of quotients do not satisfy those properties. Examples of properties which do not pass to rings of quotients include: Abelian, Dedekin
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::c4d91cab3c07ccf75b75fac038c821f4
https://doi.org/10.1016/j.jalgebra.2013.01.012
https://doi.org/10.1016/j.jalgebra.2013.01.012
Publikováno v:
Journal of Algebra and Its Applications. 10:623-642
Given a ring $R$, we study the bimodules $M$ for which the trivial extension $R\propto M$ is morphic. We obtain a complete characterization in the case where $R$ is left perfect, and we prove that $R\propto Q/R$ is morphic when $R$ is a commutative r
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::576369555640c322ac49a3e953332552
https://doi.org/10.1142/s021949881100480x
https://doi.org/10.1142/s021949881100480x
Publikováno v:
Journal of Pure and Applied Algebra. 212(1):281-296
We will completely characterize the commutative local rings for which M n ( R ) is strongly clean, in terms of factorization in R [ t ] . We also obtain similar elementwise results which show additionally that for any monic polynomial f ∈ R [ t ] ,
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::d70aaf5a44fe25fcef857433efceafda