Hostname: page-component-cd9895bd7-p9bg8 Total loading time: 0 Render date: 2024-12-28T03:33:38.421Z Has data issue: false hasContentIssue false
  • English
  • Français

Semigroup Algebras and Maximal Orders

Published online by Cambridge University Press:  20 November 2018

Eric Jespers  and
Jan Okniński
Eric Jespers
Affiliation:
Department of Mathematics and Statistics Memorial University of Newfoundland St. John’s A1C 5S7 Newfoundland, Canada
Jan Okniński
Affiliation:
Institute of Mathematics Warsaw University Banacha 2, 02-097 Warsaw Poland
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

We describe contracted semigroup algebras of Malcev nilpotent semigroups that are prime Noetherian maximal orders.

Keywords

16S3616H0520M25
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 42 , Issue 3 , 01 September 1999 , pp. 298 - 306
Copyright
Copyright © Canadian Mathematical Society 1999

References

[1] Anderson, D. F., The divisor class group of a semigroup ring. Comm. Algebra (5) 8 (1980), 467–476.Google Scholar
[2] Brown, K. A., Height one primes of polycyclic group rings. J. London Math. Soc. Ser. 2 (3) 32 (1985), 426–438.Google Scholar
[3] Chouinard, L. G. II, Krull semigroups and divisor class groups. Canad. J. Math. 23 (1981), 1459–1468.Google Scholar
[4] Clifford, A. H. and Preston, G. B., The Algebraic Theory of Semigroups, Vol. I. Amer. Math. Soc., Providence, RI, 1961.Google Scholar
[5] Gateva-Ivanova, T. and den Bergh, M. Van, Semigroups of I-type. J. Algebra (1) 206 (1998), 97–112.Google Scholar
[6] Gilmer, R., Commutative Semigroup Rings. University of Chicago Press, 1984.Google Scholar
[7] Jespers, E. and Okniński, J., Nilpotent semigroups and semigroup algebras. J. Algebra (3) 169 (1994), 984–1011.Google Scholar
[8] Jespers, E. and Okniński, J., Semigroup algebras that are principal ideal rings. J. Algebra 183 (1996), 837–863.Google Scholar
[9] Jespers, E. and Okniński, J., Binomial semigroups. J. Algebra (1) 202 (1998), 250–275.Google Scholar
[10] Jespers, E. and Okniński, J., Noetherian semigroup algebras. J. Algebra, to appear.Google Scholar
[11] Jespers, E. and Okniński, J., On a class of Noetherian algebras. Proc. Roy. Soc. Edinburgh Sect. A, to appear.Google Scholar
[12] Jespers, E. and Wauters, P., Principal ideal semigroup rings. Comm. Algebra 23 (1995), 5057–5076.Google Scholar
[13] Kargapolov, M. I. and Merzljakov, Ju. I., Fundamentals of the Theory of Groups. Springer-Verlag, New York, 1979.Google Scholar
[14] Marubayashi, H., Zhang, Y. and Yang, P., On the rings of theMorita context which are some well-known orders. Comm. Algebra (5) 26 (1998), 1429–1444.Google Scholar
[15] McConnell, J. C. and Robson, J. C., Noncommutative Noetherian Rings. Wiley Interscience, New York, 1987.Google Scholar
[16] Okniński, J., Semigroup Algebras. Marcel Dekker, 1991.Google Scholar
[17] Wauters, P.,On some subsemigroups of noncommutative Krull rings. Comm. Algebra (13–14) 12 (1984), 1751–1765.Google Scholar
[18] Wauters, P. and Jespers, E., Rings graded by an inverse semigroup with finitely many idempotents. Houston J. Math. (2) 15 (1989), 291–304.Google Scholar