Partial actions and quotient rings
DOI:
https://doi.org/10.4067/S0716-09172011000200006Abstract
In this paper we study the Martindale ring of α-quotients Q associated with the partial action (R,α). Among other results we extend the partial action to Q and prove that it can be identified with an ideal of Q, the Martindale ring of β-quotients of T , where (T, β) denotes the enveloping action of (R,α). We prove that, in general, (Q, β) is not the enveloping action of (Q,α) and study the relationship between the rings R, Q, T and Q. Finally, we establish some properties related to the center of Q and the extended α-centroid of R.
References
[2] J. Avila and M. Ferrero, Closed and Prime Ideals in Partial Skew Group Rings of Abelian Groups, to appear in J. Algebra Appl., DOI N 10.1142/S0219498811005063.
[3] W. Cortes, Partial Skew Polynomial Rings and Jacobson Rings, Comm. Algebra 38 (4), pp. 1526-1548, (2010).
[4] W. Cortes, M. Ferrero, Y. Hirano and H. Marubayashi, Partial Skew Polynomial Rings over Semisimple Artinian Rings, Comm. Algebra 38 (5), pp. 1663-1676, (2010).
[5] W. Cortes, M. Ferrero and H. Marubayashi, Partial Skew Polynomial Rings and Goldie Rings, Comm. Algebra 36 (11), pp. 4284-4295, (2008).
[6] M. Dokuchaev and R. Exel, Associativity of Crossed Products by Partial Actions, Enveloping Actions and Partial Representations, Trans. Amer. Math. Society 357 (5), pp. 1931-1952, (2005).
[7] M. Ferrero, Partial Actions of Groups on Semiprime Rings, A Series of Lectures Notes in Pure and Applied Mathematics, Volume 248, Chapman and Hall, (2006).
[8] M. Ferrero and J. Lazzarin ; Partial actions and partial skew group rings, J. Algebra 319, pp. 5247-5264, (2008).
[9] T. Y. Lam, Lectures on Modules and Rings, Graduate Text in Mathematics, Springer-Verlag, New York, (1998).
[10] M. Malásquez, Prime Ideals in Crossed Products of Abelian Groups, Comm. Algebra 22 (5), pp. 1861-1876, (1994).
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