Propiedad de Armendariz para las extensiones PBW torcidas y su anillo clásico de cocientes
Publicado 2016-12-12
Palabras clave
- Armendariz,
- Baer,
- quasi-Baer,
- p.p. y p.q.-anillos,
- extensiones torcidas de Poincaré-Birkho-Witt
Cómo citar
Derechos de autor 2016 Armando Reyes, Héctor Suárez
Esta obra está bajo una licencia internacional Creative Commons Atribución 4.0.
Resumen
Consideramos un primer acercamiento a la noción de anillo de Armendariz para una extensión torcida de Poincaré-Birkho-Witt (PBW), y su anillo clásico de cocientes. Como una aplicación inmediata de este tratamiento, estudiamos las propiedades de Baer, quasi-Baer, p.p. y p.q.-Baer para estas extensiones. De esta manera, generalizamos varios resultados de la literatura para extensiones de Ore y extensiones PBW torcidas.
Para citar este artículo: A. Reyes, H. Suárez, Armendariz property for skew PBW extensions and their classical ring of quotients, Rev. Integr. Temas Mat. 34 (2016), No. 2, 147-168.
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Referencias
- Anderson D.D. and Camillo V., "Armendariz rings and Gaussian rings", Comm. Algebra 26 (1998), No. 7, 2265-2272.
- Armendariz E.P., "A note on extensions of Baer and p.p.-rings", J. Aust. Math. Soc. 18, (1974), 470-473.
- Armendariz E.P., Koo H.K. and Park J.K., "Isomorphic Ore extensions", Comm. Algebra 15 (1987), No. 12, 2633-2652.
- Birkenmeier G.F., "Baer rings and quasi-continuous rings have a MDSN", Pacific J. Math. 97 (1981), No. 2, 283-292.
- Birkenmeier G.F., Kim J.Y. and Park J.K., "Polynomial extensions of Baer and quasi-Baer rings", J. Pure Appl. Algebra 159 (2001), No. 1, 25-42.
- Birkenmeier G.F., Kim J.Y. and Park J.K., "Principally quasi-Baer rings", Comm. Algebra 29 (2001), No. 2, 639-660.
- Chen W. and Tong W., "A note on skew Armendariz rings", Comm. Algebra 33 (2005), No. 4, 1137-1140.
- Clark W.E., "Twisted matrix units semigroup algebras", Duke Math. J. 34 (1967), 417-423.
- Gallego C. and Lezama O., "Gröbner bases for ideals of σ-PBW extensions", Comm. Algebra 39 (2011), No. 1, 50-75.
- Han J., Hirano Y. and Kim H., "Semiprime Ore extensions", Comm. Algebra 28 (2000), No. 8, 3795-3801.
- Han J., Hirano Y. and Kim H., "Some results on skew polynomial rings over a reduced ring", in International Symposium on Ring Theory (Kyongju, 1999), Trends Math., Birkhäuser Boston, Boston, MA, (2001), 123-129.
- Hong C.Y., Kim N.K. and Kwak T.K., "On skew Armendariz rings", Comm. Algebra 31 (2003), No. 1, 103-122.
- Hong C.Y., Kim N.K. and Kwak T.K., "Ore extensions of Baer and p.p.-rings", J. Pure Appl. Algebra 151 (2000), No. 3, 215-226.
- Huh C., Lee Y. and Smoktunowicz A., "Armendariz rings and semicommutative rings", Comm. Algebra 30 (2002), No. 2, 751-761.
- Jategaonkar A.V., Localization in Noetherian rings, London Mathematical Society Lecture Note Series, 98, Cambridge University Press, Cambridge, 1986.
- Kaplansky I., Rings of operators. W.A. Benjamin, Inc., New York-Amsterdam, 1968.
- Kim N.K. and Lee Y., "Armendariz rings and reduced rings", J. Algebra 223 (2000), No. 2, 477-488.
- Krempa J., "Some examples of reduced rings", Algebra Colloq. 3 (1996), No. 4, 289-300.
- Lee T-K. and Wong T-L., "On Armendariz rings", Houston J. Math. 29 (2003), No. 3, 583-593.
- Lezama O., Acosta J.P. and Reyes A., "Prime ideals of skew PBW extensions", Rev. Un. Mat. Argentina 56 (2015), No. 2, 39-55.
- Lezama O., Acosta J.P., Chaparro C., Ojeda I. and Venegas C., "Ore and Goldie theorems for skew PBW extensions", Asian-Eur. J. Math. 6 (2013), No. 4, 20 pp.
- Lezama O. and Reyes A., "Some homological properties of skew PBW extensions", Comm. Algebra 42 (2014), No. 3, 1200-1230.
- Matczuk J., "A characterization of σ-rigid rings", Comm. Algebra 32 (2004), No. 11, 4333-4336.
- Nasr-Isfahani A.R. and Moussavi A., "On classical quotient rings of skew Armendariz rings", Int. J. Math. Math. Sci. (2007), 7 pp.
- Rege M.B. and Chhawchharia S., "Armendariz rings", Proc. Japan Acad. Ser. A Math. Sci. 73 (1997), No. 1, 14-17.
- Reyes A., "Gelfand-Kirillov dimension of skew PBW extensions"', Rev. Colombiana Mat. 47 (2013), No. 1, 95-111.
- Reyes A., "Jacobson's conjecture and skew PBW extensions", Rev. Integr. Temas Mat. 32 (2014), No. 2, 139-152.
- Reyes A., "Skew PBW extensions of Baer, quasi-Baer, p.p. and p.q.-rings", Rev. Integr. Temas Mat. 33 (2015), No. 2, 173-189.
- Reyes A., "Uniform dimension over skew PBW extensions", Rev. Colombiana Mat. 48 (2014), No. 1, 79-96.
- Suárez H., Lezama O. and Reyes A., "Some Relations between N-Koszul, Artin-Schelter Regular and Calabi-Yau algebras with Skew PBW Extensions", Ciencia en Desarrollo 6 (2015), No. 2, 205-213.