114
Views
7
CrossRef citations to date
0
Altmetric
Original Articles

Semiprimeness, quasi-Baerness and prime radical of skew generalized power series rings

&
Pages 2306-2324 | Received 15 May 2015, Published online: 07 Oct 2016

References

  • Armendariz, E. P. (1974). A note on extensions of Baer and p.p.-rings. J. Austral. Math. Soc. 18:470–473.
  • Bell, A. D. (1985). When are all prime ideals in an Ore extension Goldie? Commun. Algebra 13(8):1743–1762.
  • Bell, H. E. (1970). Near-rings in which each element is a power of itself. Bull. Aust. Math. Soc. 2:363–368.
  • Berberian, S. K. (1972). Baer ∗-Rings. Berlin-Heidelberg-New York: Springer-Verlag.
  • Bergman, G. M., Issacs, I. M. (1973). Rings with fixed-point-free group actions. Proc. Lond. Math. Soc. 27:69–87.
  • Birkenmeier, G. F., Heatherly, H. E., Kim, J. Y., Park, J. K. (2000). Triangular matrix representations. J. Algebra 230:558–595.
  • Birkenmeier, G. F., Kim, J. Y., Park, J. K. (2001). Principally quasi-Baer rings. Commun. Algebra 29(2):639–660.
  • Birkenmeier, G. F., Park, J. K. (2003). Triangular matrix representations of ring extensions. J. Algebra 265(2):457–477.
  • Birkenmeier, G. F., Park, J. K., Rizvi, S. T. (2002). Generalized triangular matrix rings and the fully invariant extending property. Rocky Mount. J. Math. 32(4):1299–1319.
  • Chatters, A. W., Hajarnavis, C. R. (1980). Rings with Chain Conditions. London: Pitman Advanced Publishing Program.
  • Clark, W. E. (1967). Twisted matrix units semigroup algebras. Duke Math. J. 34:417–424.
  • Cohn, P. M. (1982). A Morita context related to finite automorphism groups of rings. Pacific J. Math. 98(1):37–54.
  • Cohn, P. M. (1985). Free Rings and Their Relations. 2nd ed. London: Academic Press.
  • Connell, I. G. (1963). On the group ring. Canad. J. Math. 15:650–685.
  • Elliott, G. A., Ribenboim, P. (1990). Fields of generalized power series. Arch. Math. 54:365–371.
  • Fisher, J. W., Montgomery, S. (1978). Semiprime skew group rings. J. Algebra 52(1):241–247.
  • Habibi, M., Moussavi, A., Manaviyat, R. (2010). On skew quasi-Baer rings. Commun. Algebra 38(10):3637–3648.
  • Herstein, I. N., Small, L. W. (1964). Nil rings satisfying certain chain conditions. Canad. J. Math. 16:771–776.
  • Hirano, Y. (2001). On ordered monoid rings over a quasi-Baer ring. Commun. Algebra 29:2089–2095.
  • Huh, C., Kim, H. K., Lee, D. S., Lee, Y. (2001). Prime radicals of formal power series ring. Bull. Korean Math. Soc. 38(4):623–633.
  • Irving, R. S. (1979). Prime ideals of Ore extensions over commutative rings. J. Algebra 56:315–342.
  • Jin, H. L., Doh, J., Park, J. K. (2009). Group actions on Quasi-Baer rings. Canad. Math. Bull. 52(4):564–582.
  • Jordan, D. A. (1982). Bijective extensions of injective ring endomorphisms. J. Lond. Math. Soc. 25(2):435–448.
  • Kaplansky, I. (1951). Projections in Banach algebras. Ann. Math. 53:235–249.
  • Kaplansky, I. (1965). Rings of Operators. New York: Benjamin.
  • Lam, T. Y. (1991). A First Course in Noncommutative Rings. New York: Springer-Verlag.
  • Lam, T. Y., Leroy, A., Matczuk, J. (1997). Primeness, semiprimeness and prime radical of Ore extensions. Commun. Algebra 25(8):2459–2506.
  • Lanski, C. (1969). Nil subrings of Goldie rings are nilpotent. Canad. J. Math. 21:904–907.
  • Lenagan, T. H. (1974). Nil ideals in rings with finite Krull dimension. J. Algebra 29:77–87.
  • Letzter, E. S., Wang, L. (2012). Goldie ranks of skew power series rings of automorphic type. Commun. Algebra 40(6):1911–1917.
  • Liu, Z. K. (2006). Triangular matrix representations of rings of generalized power series. Acta Math. Sinica (English Series) 22:989–998.
  • Marks, G. (2002). Reversible and symmetric rings. J. Pure Appl. Algebra 174(3):311–318.
  • Marks, G., Mazurek, R., Ziembowski, M. (2009). A new class of unique product monoids with applications to ring theory. Semigroup Forum 78(2):210–225.
  • Marks, G., Mazurek, R., Ziembowski, M. (2010). A unified approach to various generalizations of Armendariz rings. Bull. Aust. Math. Soc. 81:361–397.
  • Mazurek, R. (2015). Left principally quasi-Baer and left APP-rings of skew generalized power series. J. Algebra Appl. 14(3): 1550038, 36 pp.
  • Mazurek, R., Ziembowski, M. (2008). On Von Neumann regular rings of skew generalized power series. Commun. Algebra 36(5):1855–1868.
  • Montgomery, S. (1978). Outer automorphisms of semiprime rings. J. Lond. Math. Soc. 18(2):209–220.
  • Passman, D. S. (1977). The Algebraic Structure of Group Rings. New York: Wiley.
  • Paykan, K., Moussavi, A. (2016). Baer and quasi-Baer skew generalized power series rings. Commun. Algebra 44(4):1615–1635.
  • Pearson, K. R., Stephenson, W. (1977). A skew polynomial ring over a Jacobson ring need not be a Jacobson ring. Commun. Algebra 5:783–94.
  • Pollingher, A., Zaks, A. (1970). On Baer and quasi-Baer rings. Duke Math. J. 37:127–138.
  • Ribenboim, P. (1992). Noetherian rings of generalized power series. J. Pure Appl. Algebra 79(3):293–312.
  • Ribenboim, P. (1995). Some examples of valued fields. J. Algebra 173:668–678.
  • Ribenboim, P. (1995). Special properties of generalized power series. J. Algebra 173:566–586.
  • Ribenboim, P. (1997). Semisimple rings and von Neumann regular rings of generalized power series. J. Algebra 198:327–338.
  • Rickart, C. E. (1946). Banach algebras with an adjoint operation. Ann. Math. 47:528–550.
  • Rowen, L. H. (1988). Ring Theory I. New York: Academic Press.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.