## Rocky Mountain Journal of Mathematics

### Partial crossed products and fully weakly prime rings

#### Abstract

In this paper, we study the necessary and sufficient conditions for the partial crossed product to be a fully weakly prime ring. Moreover, we give a description of the prime radical of the partial crossed product when the base ring is a fully weakly prime ring.

#### Article information

Source
Rocky Mountain J. Math., Volume 46, Number 4 (2016), 1107-1139.

Dates
First available in Project Euclid: 19 October 2016

https://projecteuclid.org/euclid.rmjm/1476884578

Digital Object Identifier
doi:10.1216/RMJ-2016-46-4-1107

Mathematical Reviews number (MathSciNet)
MR3563177

Zentralblatt MATH identifier
1383.16026

#### Citation

Cortes, Wagner; Soares, Marlon. Partial crossed products and fully weakly prime rings. Rocky Mountain J. Math. 46 (2016), no. 4, 1107--1139. doi:10.1216/RMJ-2016-46-4-1107. https://projecteuclid.org/euclid.rmjm/1476884578

#### References

• W.D. Blair and H. Tsutsui, Fully prime rings, Comm. Alg. 22 (1994), 5388–5400.
• P. Carvalho, W. Cortes and M. Ferrero, Partial skew group rings over polycyclic by finite groups, Alg. Rep. Th. 14 (2011), 449–462.
• E. Cisneros, M. Ferrero and M.I. Conzáles, Prime ideals of skew polynomial rings and skew Laurent polynomial rings, Math. J. Okayama Univ. 32 (2007), 61–72.
• W. Cortes, Partial skew polynomial rings and Jacobson rings, Comm. Alg. 38 (2010), 1526–1548.
• W. Cortes and M. Ferrero, Partial skew polynomial rings: Prime and maximal ideals, Comm. Alg. 35 (2007), 1183–1199.
• M. Dokuchaev, A. del Rio and J.J. Simón, Globalizations of partial actions on nonunital rings, Proc. Amer. Math. Soc. 135 (2007), 343–352.
• M. Dokuchaev and R. Exel, Associativity of crossed products by partial actions, enveloping actions and partial representations, Trans. Amer. Math. Soc. 357 (2005), 1931–1952.
• M. Dokuchaev, R. Exel and J.J. Simón, Crossed products by twisted and graded algebras, J. Alg. 320 (2008), 3278–3310.
• ––––, Globalization of twisted partial actions, Trans. Amer. Math. Soc. 362 (2010), 4137–4160.
• M. Dokuchaev, M. Ferrero and A. Paques, Partial actions and Galois theory, J. Pure Appl. Alg. 208 (2007), 77–87.
• R. Exel, Twisted partial actions: A classification of regular C*-algebraic bundles, Proc. Lond. Math. Soc. 74 (1997), 417–443.
• R. Exel, M. Laca and J. Quigg, Partial dynamical system and C*-algebras generated by partial isometries, J. Oper. Theor. 47 (2002), 169–186.
• M. Ferrero and J. Lazzarin, Partial actions and partial skew group rings, J. Alg. 139 (2008), 5247–5264.
• Y. Hirano, E. Poon and H. Tsutsui, On rings in which every ideal is weakly prime, Bull. Korean Math. Soc. 47 (2010), 1077–1087.
• L. Huang and Z. Yi, Crossed products and full prime rings, in Advances in ring theory, Proc. $4$th China-Japan-Korea Intl. Conf., 2005.
• T.Y. Lam, A first course in noncommutative rings, Springer-Verlag, New York, 2001.
• K. McClanahan, $K$-theory for partial crossed products by discrete groups, J. Funct. Anal. 130 (1995), 77–117.
• D.S. Passman, Infinite crossed products, Academic Press, Cambridge, MA, 1980.
• K.R. Pearson, W. Stephenson and J.F. Watters, Skew polynomials and Jacobson rings, Proc. Lond. Math. Soc. 42 (1981), 559–576.
• J.C. Quigg and I. Raeburn, Characterizations of crossed products by partial actions, J. Oper. Th. 37 (1997), 311–340.
• H. Tsutsui, Fully prime rings II, Comm. Alg. 24 (1996), 2981–2989.