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Proceedings of the Estonian Academy of Sciences

ISSN 1736-7530 (electronic)   ISSN 1736-6046 (print)
Formerly: Proceedings of the Estonian Academy of Sciences, series Physics & Mathematics and  Chemistry
Published since 1952

Proceedings of the Estonian Academy of Sciences

ISSN 1736-7530 (electronic)   ISSN 1736-6046 (print)
Formerly: Proceedings of the Estonian Academy of Sciences, series Physics & Mathematics and  Chemistry
Published since 1952
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Commutativity and ideals in category crossed products; pp. 338–346

(Full article in PDF format) doi: 10.3176/proc.2010.4.13


Authors

Johan Öinert, Patrik Lundström

Abstract

In order to simultaneously generalize matrix rings and group graded crossed products, we introduce category crossed products. For such algebras we describe the centre and the commutant of the coefficient ring. We also investigate the connection between on the one hand maximal commutativity of the coefficient ring and on the other hand nonemptiness of intersections of the coefficient ring by nonzero two-sided ideals.

Keywords

category graded rings, crossed products, ideals.

References

  1. Caenepeel , S. and Van Oystaeyen , F. Brauer Groups and the Cohomology of Graded Rings. Monographs and Textbooks in Pure and Applied Mathematics , vol. 121. Marcel Dekker , Inc. , New York , 1988.

  2. Cohen , M. and Montgomery , S. Group-graded rings , smash products and group actions. Trans. Amer. Math. Soc. , 1984 , 282(1) , 237–258.
doi:10.2307/1999586

  3. Fisher , J. W. and Montgomery , S. Semiprime skew group rings. J. Algebra , 1978 , 52(1) , 241–247.
doi:10.1016/0021-8693(78)90272-7

  4. Higgins , P. J. Notes on Categories and Groupoids. Van Nostrand , 1971.

  5. Irving , R. S. Prime ideals of Ore extensions over commutative rings. J. Algebra , 1979 , 56(2) , 315–342.
doi:10.1016/0021-8693(79)90341-7

  6. Irving , R. S. Prime ideals of Ore extensions over commutative rings II. J. Algebra , 1979 , 58(2) , 399–423.
doi:10.1016/0021-8693(79)90169-8

  7. Karpilovsky , G. The Algebraic Structure of Crossed Products. North-Holland Mathematics Studies , vol. 142. Notas de Matemįtica , vol. 118. North-Holland , Amsterdam , 1987.

  8. Kelarev , A. V. Ring Constructions and Applications. Series in Algebra , vol. 9. World Scientific Publishing Co. , 2002.

  9. Launois , S. , Lenagan , T. H. , and Rigal , L. Quantum unique factorisation domains. J. London Math. Soc. (2) , 2006 , 74(2) , 321–340.

10. Lorenz , M. and Passman , D. S. Prime ideals in crossed products of finite groups. Israel J. Math. , 1979 , 33(2) , 89–132.
doi:10.1007/BF02760553

11. Lorenz , M. and Passman , D. S. Addendum – Prime ideals in crossed products of finite groups. Israel J. Math. , 1980 , 35(4) , 311–322.
doi:10.1007/BF02760656

12. Lundström , P. Crossed product algebras defined by separable extensions. J. Algebra , 2005 , 283 , 723–737.
doi:10.1016/j.jalgebra.2004.09.007

13. Lundström , P. Separable groupoid rings. Comm. Algebra , 2006 , 34 , 3029–3041.
doi:10.1080/00927870600639906

14. Lundström , P. Strongly groupoid graded rings and cohomology. Colloq. Math. , 2006 , 106 , 1–13.
doi:10.4064/cm106-1-1

15. Mac Lane , S. Categories for the Working Mathematician. Graduate Texts in Mathematics , vol. 5. Springer-Verlag , New York , 1998.

16. Montgomery , S. and Passman , D. S. Crossed products over prime rings. Israel J. Math. , 1978 , 31(3–4) , 224–256.
doi:10.1007/BF02761494

17. Nǎstǎsescu , C. and Van Oystaeyen , F. Graded Ring Theory. North-Holland Publishing Co. , Amsterdam–New York , 1982.

18. Öinert , J. and Silvestrov , S. D. Commutativity and ideals in algebraic crossed products. J. Gen. Lie T. Appl. , 2008 , 2(4) , 287–302.
doi:10.4303/jglta/S070404

19. Öinert , J. and Silvestrov , S. D. On a correspondence between ideals and commutativity in algebraic crossed products. J. Gen. Lie T. Appl. , 2008 , 2(3) , 216–220.

20. Öinert , J. and Silvestrov , S. D. Crossed product-like and pre-crystalline graded rings. In Generalized Lie Theory in Mathematics , Physics and Beyond (Silvestrov , S. , Paal , E. , Abramov , V. , and Stolin , A. , eds). Springer-Verlag , Berlin , Heidelberg , 2009 , 281–296.
doi:10.1007/978-3-540-85332-9_24

21. Öinert , J. and Silvestrov , S. Commutativity and ideals in pre-crystalline graded rings. Acta Appl. Math. , 2009 , 108(3) , 603–615.
doi:10.1007/s10440-009-9434-4

22. Öinert , J. , Silvestrov , S. D. , Theohari-Apostolidi , T. , and Vavatsoulas , H. Commutativity and ideals in strongly graded rings. Acta Appl. Math. , 2009 , 108(3) , 585–602.
doi:10.1007/s10440-009-9435-3

23. Passman , D. S. The Algebraic Structure of Group Rings. Pure and Applied Mathematics. Wiley-Interscience (John Wiley & Sons) , New York–London–Sydney , 1977.
 
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Current Issue: Vol. 67, Issue 3 in Press, 2018




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No. 1: 20 March
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