Annihilating properties of ideals generated by coefficients of polynomials and power series

Autor: Nam Kyun Kim, Yang Lee, Michał Ziembowski

Publikováno v: International Journal of Algebra and Computation. 32:237-249

In this paper, we study the annihilating properties of ideals generated by coefficients of polynomials and power series which satisfy a structural equation. We first show that if [Formula: see text] for polynomials [Formula: see text] over any ring [

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::ac92540bbf2fa97c55302381cef0b1a1
https://doi.org/10.1142/s0218196722500114

Construction of a class of maximal commutative subalgebras of prime Leavitt path algebras

Autor: Leon van Wyk, Grzegorz Bajor, Michał Ziembowski

Publikováno v: Forum Mathematicum. 33:1573-1590

Considering prime Leavitt path algebras L K ⁢ ( E ) {L_{K}(E)} , with E being an arbitrary graph with at least two vertices, and K being any field, we construct a class of maximal commutative subalgebras of L K ⁢ ( E ) {L_{K}(E)} such that, for e

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::189ac596708e185597fb8441ab3774bc
https://doi.org/10.1515/forum-2020-0213

Lie properties in associative algebras

Autor: Szilvia Homolya, Leon van Wyk, Jeno Szigeti, Michał Ziembowski

Publikováno v: Journal of Algebra. 573:492-508

For a field K containing 1 2 , we exhibit two matrices in the full n × n matrix algebra M n ( K ) which generate M n ( K ) as a Lie K-algebra with the commutator Lie product. We also study Lie centralizers of a not necessarily commutative unitary al

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::1f14399163b04d5558239e0e3fddd0e9
https://doi.org/10.1016/j.jalgebra.2021.01.002

Annihilator condition does not pass to polynomials and power series

Autor: Michał Ziembowski, Grzegorz Bajor

Publikováno v: Journal of Pure and Applied Algebra. 223:3869-3878

In this paper we construct a ring A which has annihilator condition (a.c.) and we show that neither A [ x ] nor A [ [ x ] ] has this property. This answers in negative a question asked by Hong, Kim, Lee and Nielsen. We also show that there is an alge

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::6ac13d55f2ded0bbeaca41ed01596164
https://doi.org/10.1016/j.jpaa.2018.12.009

Five solved problems on radicals of Ore extensions

Autor: Michał Ziembowski, Be'eri Greenfeld, Agata Smoktunowicz

Publikováno v: Recercat: Dipósit de la Recerca de Catalunya
Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya)
Recercat. Dipósit de la Recerca de Catalunya
instname
Dipòsit Digital de Documents de la UAB
Universitat Autònoma de Barcelona
Publ. Mat. 63, no. 2 (2019), 423-444
Greenfeld, B, Smoktunowicz, A & Ziembowski, M 2019, ' Five solved problems on radicals of Ore extensions ', Publicacions Matemàtiques, vol. 63, no. 2, pp. 423-444 . https://doi.org/10.5565/PUBLMAT6321902
Publicacions Matemàtiques; Vol. 63, Núm. 2 (2019); p. 423-444

The first named author was partially supported by an ISF grant #1623/16. The second named author was supported by ERC Advanced grant Coimbra 320974. The third named author was supported by the Polish National Science Centre grant UMO2017/25/B/ST1/003

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::279696dfb7e5cc21f632fa72c3d88c4c
https://doi.org/10.5565/publmat6321902