caa a22 4500 606160809 CHVBK 20210128100631.0 cr unu---uuuuu 210128e20150601xx s 000 0 eng 10.1007/s10468-015-9516-0 doi (NATIONALLICENCE)springer-10.1007/s10468-015-9516-0 Chains of Prime Ideals and Primitivity of ℤ $\mathbb {Z}$ -Graded Algebras [Elektronische Daten] [Be'eri Greenfeld, André Leroy, Agata Smoktunowicz, Michał Ziembowski] In this paper we provide some results regarding affine, prime, ℤ $\mathbb {Z}$ -graded algebras R = ⊕ i ∈ ℤ R i $R=\bigoplus _{i\in \mathbb {Z}}R_{i}$ generated by elements with degrees 1,−1 and 0, with R 0 finite-dimensional. The results are as follows. These algebras have a classical Krull dimension when they have quadratic growth. If R k ≠0 for almost all k then R is semiprimitive. If in addition R has GK dimension less than 3 then R is either primitive or PI. The tensor product of an arbitrary Brown-McCoy radical algebra of Gelfand Kirillov dimension less than three and any other algebra is Brown-McCoy radical. Springer Science+Business Media Dordrecht, 2015 Graded algebras nationallicence Primitive rings nationallicence Semiprimitive rings nationallicence Brown-McCoy radical nationallicence Chains of prime ideals nationallicence GK dimension nationallicence Growth of algebra nationallicence Greenfeld Be'eri Department of Mathematics, Bar Ilan University, 5290002, Ramat Gan, Israel aut Leroy André Faculté Jean Perrin, Rue J. Souvraz, Université d'Artois, 62300, Lens, France aut Smoktunowicz Agata Maxwell Institute for Mathematical Sciences, School of Mathematics, University of Edinburgh, JCM Building, Kings Buildings, Mayfield Road, EH9 3JZ, Edinburgh, Scotland, UK aut Ziembowski Michał Faculty of Mathematics and Information Science, Warsaw University of Technology, 00-662, Warsaw, Poland aut Algebras and Representation Theory Springer Netherlands 18/3(2015-06-01), 777-800 1386-923X 18:3<777 2015 18 10468 https://doi.org/10.1007/s10468-015-9516-0 text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s10468-015-9516-0 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Greenfeld Be'eri Department of Mathematics, Bar Ilan University, 5290002, Ramat Gan, Israel aut NATIONALLICENCE 700 1- Leroy André Faculté Jean Perrin, Rue J. Souvraz, Université d'Artois, 62300, Lens, France aut NATIONALLICENCE 700 1- Smoktunowicz Agata Maxwell Institute for Mathematical Sciences, School of Mathematics, University of Edinburgh, JCM Building, Kings Buildings, Mayfield Road, EH9 3JZ, Edinburgh, Scotland, UK aut NATIONALLICENCE 700 1- Ziembowski Michał Faculty of Mathematics and Information Science, Warsaw University of Technology, 00-662, Warsaw, Poland aut NATIONALLICENCE 773 0- Algebras and Representation Theory Springer Netherlands 18/3(2015-06-01), 777-800 1386-923X 18:3<777 2015 18 10468