View More View Less
  • 1 Alexandria University, Alexandria, Egypt
Restricted access

Purchase article

USD  $25.00

1 year subscription (Individual Only)

USD  $800.00

The consistent way of investigating rings with involution, briefly *-rings, is to study them in the category of *-rings with morphisms preserving also involution. In this paper we continue the study of *-rings and the notion of *-reduced *-rings is introduced and their properties are studied. We introduce also the class of *-Baer *-rings. This class is defined in terms of *-annihilators and principal *-biideals, and it naturally extends the class of Baer *-rings. The use of *-biideals makes this concept more consistent with the involution than the use of right ideals in the notion of Baer *-rings. We prove that each *-Baer *-ring is semiprime. Moreover, we show that the property of *-Baer extends to both the *-corner and the center of the *-ring. Finally, we discuss the relation between *-Baer and quasi-Baer *-rings; the generalization of Baer *-ring.

  • 1

    Aburawash, U. A., Usama A., Semiprime involution rings and chain conditions, Contr. to General Algebra 7, Hölder—Pichler—Tempsky, Wien and B. G. Teubner, Stuttgart (1991), 711.

    • Search Google Scholar
    • Export Citation
  • 2

    Aburawash, U. A., Usama A., On involution rings, East-West J. Math., 2(2) (2000), 109126.

  • 3

    Aburawash, U. A. and Sola, K. B., *-Zero divisors and *-prime ideals, East-West J. Math., 12(1) (2010), 2731.

  • 4

    Beidar, K. I. and Wiegandt, R., Rings with involution and chain conditions, J. Pure and Appl. Algebra, 87 (1993), 205220.

  • 5

    Beidar, K. I., Márki, L., Mlitz, R. and Wiegandt, R., Primitive involution rings, Acta Math. Hungar., 109 (2005), 357368.

  • 6

    Berberian, S. K., Baer *-Rings, Grundlehren Math. Wiss. Band. 195, Springer-Verlag, Berlin–Heidelberg–New York, 1972.

  • 7

    Berberian, S. K., Baer Rings and Baer *-Rings, The University of Texas at Austin, March 1988.

  • 8

    Birkenmeier, G. F. and Groenewald, N. J., Prime ideals in rings with involution, Quaestiones in Mathematicae, 20 (1997), 591603.

  • 9

    Birkenmeier, G. F. and Park, J. K., Self-adjoint ideals in Baer *-ring, Comm. Algebra, 28 (2000), 42594268.

  • 10

    Birkenmeier, G. F., Kim, J. Y. and Park, J. K., On Quasi-Baer rings, Contemporary Mathematics, 259 (2000), 6792.

  • 11

    Birkenmeier, G. F., Kim, J. Y. and Park, J. K., Polynomial extensions of Baer and quasi-Baer rings, J. Pure Appl. Algebra, 159 (2001), 2542.

    • Search Google Scholar
    • Export Citation
  • 12

    Birkenmeier, G. F., Park, J. K. and Rizvi, S. T., Hulls of semiprime rings with applications to C*-Algebra, J. Algebra, 322 (2009), 327352.

    • Search Google Scholar
    • Export Citation
  • 13

    Herstein, I. N., Rings with Involution, Univ. Chicago Press, 1976.

  • 14

    Kaplansky, I., Rings of Operators, Benjamin, New York, 1968.

  • 15

    Rowen, L. H., Ring Theory I, Academic Press, San Diego, 1988.

  • 16

    Lee, Y., Kim, N. K. and Hong, C. Y., Counterexamples on Baer rings, Comm. Algebra, 25 (1997), 497507.

The author instruction is available in PDF.

Please, download the file from HERE

Manuscript submission: HERE


  • Impact Factor (2019): 0.486
  • Scimago Journal Rank (2019): 0.234
  • SJR Hirsch-Index (2019): 23
  • SJR Quartile Score (2019): Q3 Mathematics (miscellaneous)
  • Impact Factor (2018): 0.309
  • Scimago Journal Rank (2018): 0.253
  • SJR Hirsch-Index (2018): 21
  • SJR Quartile Score (2018): Q3 Mathematics (miscellaneous)

Language: English, French, German

Founded in 1966
Publication: One volume of four issues annually
Publication Programme: 2020. Vol. 57.
Indexing and Abstracting Services:

  • CompuMath Citation Index
  • Mathematical Reviews
  • Referativnyi Zhurnal/li>
  • Research Alert
  • Science Citation Index Expanded (SciSearch)/li>
  • The ISI Alerting Services


Subscribers can access the electronic version of every printed article.

Senior editors

Editor(s)-in-Chief: Pálfy Péter Pál

Managing Editor(s): Sági, Gábor

Editorial Board

  • Biró, András (Number theory)
  • Csáki, Endre (Probability theory and stochastic processes, Statistics)
  • Domokos, Mátyás (Algebra (Ring theory, Invariant theory))
  • Győri, Ervin (Graph and hypergraph theory, Extremal combinatorics, Designs and configurations)
  • O. H. Katona, Gyula (Combinatorics)
  • Márki, László (Algebra (Semigroup theory, Category theory, Ring theory))
  • Némethi, András (Algebraic geometry, Analytic spaces, Analysis on manifolds)
  • Pach, János (Combinatorics, Discrete and computational geometry)
  • Rásonyi, Miklós (Probability theory and stochastic processes, Financial mathematics)
  • Révész, Szilárd Gy. (Analysis (Approximation theory, Potential theory, Harmonic analysis, Functional analysis))
  • Ruzsa, Imre Z. (Number theory)
  • Soukup, Lajos (General topology, Set theory, Model theory, Algebraic logic, Measure and integration)
  • Stipsicz, András (Low dimensional topology and knot theory, Manifolds and cell complexes, Differential topology)
  • Szász, Domokos (Dynamical systems and ergodic theory, Mechanics of particles and systems)
  • Tóth, Géza (Combinatorial geometry)

Gábor Sági
Address: P.O. Box 127, H–1364 Budapest, Hungary
Phone: (36 1) 483 8344 ---- Fax: (36 1) 483 8333