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MONOID ALGEBRAS OVER NON-COMMUTATIVE RINGS

Year 2007, Volume: 2 Issue: 2, 25 - 53, 01.12.2007

E. P. Cojuhari

Abstract

We define on an arbitrary ring A a family of mappings (σx,y) subscripted with elements of a multiplicative monoid G. The assigned properties allow to call these mappings as derivations of the ring A. Beside the general situation it is given their description for the case of a partially ordered monoid. A monoid algebra of G over A is constructed explicitly, and the universality property of it is shown. The notion of a monoid algebra in our context extends those of a group ring, a skew polynomial ring, Weyl algebra and other related ones. The connection with crossed products is also shown.

Keywords

Derivations monoid algebras free algebras skew polynomial rings

References

  • L. Bonami, On the structure of skew group rings, M¨unchen: Verlag R. Fischer, A.A. Bovdi, Group rings. Kiev UMK VO. (Russian), 1988.
  • A.A. Bovdi, Crossed products of a semigroup and a ring. Sibirsk. Mat. Zh. 4 (1963), 481-499.
  • P.M. Cohn, Free rings and their relations. Academic Press, London, New-York, C. Faith, Algebra: rings, modules and categories I. Springer-Verlag, Berlin, Heidelberg, New-York, 1973.
  • G. Karpilovsky, Commutative group algebras. New-York, 1983.
  • G. Karpilovsky, The algebraic structure of crossed products. Amsterdam: North-Holland, 1987.
  • S. Lang, Algebra. Addison Wesley, Reading, Massachusetts, 1970.
  • J.C. McConnell, J.C. Robson, Noncommutative Noetherian Rings. Wiley, New York, 1987.
  • O. Ore, Theory of non-commutative polynomials. Annals of Mathematics, no. (1933), 480-508.
  • D.S. Passman, The algebraic structure of group rings. Wiley-Interscience, New York , 1977.
  • D.S. Passman, InŞnite crossed products. Academic Press, Boston, 1989.
  • Yu.M. Ryabukhin, Quasi-regular algebras, modules, groups and varieties. Buletinul A.S.R.M., Matematica, no.1(23) (1997), 6-62 (Russian).
  • T.H.M. Smits, Nilpotent S - derivations. Indag. Math. 30 (1968), 72-86.
  • T.H.M. Smits, Skew polynomial rings. Indag. Math. 30 (1968), 209-224.
  • T.H.M. Smits, The free product of a quadratic number Şeld and semiŞeld. Indag. Math., 31 (1969), 145-159.
  • A.E. Zalesskii, A.V. Mihalev, Group rings. in: Itogi Nauki i Tech., Ser. ”Sovr. probl. mat.”, vol.2, M., 1973 (Russian). E. P. Cojuhari
  • Department of Mathematical Modelling and Economical Informatics, State University of Moldova, str. A. Mateevici 60, MD-2009, Chisinau, Moldova
  • E-mail: cojuhari@usm.md

Year 2007, Volume: 2 Issue: 2, 25 - 53, 01.12.2007

E. P. Cojuhari

Abstract

References

  • L. Bonami, On the structure of skew group rings, M¨unchen: Verlag R. Fischer, A.A. Bovdi, Group rings. Kiev UMK VO. (Russian), 1988.
  • A.A. Bovdi, Crossed products of a semigroup and a ring. Sibirsk. Mat. Zh. 4 (1963), 481-499.
  • P.M. Cohn, Free rings and their relations. Academic Press, London, New-York, C. Faith, Algebra: rings, modules and categories I. Springer-Verlag, Berlin, Heidelberg, New-York, 1973.
  • G. Karpilovsky, Commutative group algebras. New-York, 1983.
  • G. Karpilovsky, The algebraic structure of crossed products. Amsterdam: North-Holland, 1987.
  • S. Lang, Algebra. Addison Wesley, Reading, Massachusetts, 1970.
  • J.C. McConnell, J.C. Robson, Noncommutative Noetherian Rings. Wiley, New York, 1987.
  • O. Ore, Theory of non-commutative polynomials. Annals of Mathematics, no. (1933), 480-508.
  • D.S. Passman, The algebraic structure of group rings. Wiley-Interscience, New York , 1977.
  • D.S. Passman, InŞnite crossed products. Academic Press, Boston, 1989.
  • Yu.M. Ryabukhin, Quasi-regular algebras, modules, groups and varieties. Buletinul A.S.R.M., Matematica, no.1(23) (1997), 6-62 (Russian).
  • T.H.M. Smits, Nilpotent S - derivations. Indag. Math. 30 (1968), 72-86.
  • T.H.M. Smits, Skew polynomial rings. Indag. Math. 30 (1968), 209-224.
  • T.H.M. Smits, The free product of a quadratic number Şeld and semiŞeld. Indag. Math., 31 (1969), 145-159.
  • A.E. Zalesskii, A.V. Mihalev, Group rings. in: Itogi Nauki i Tech., Ser. ”Sovr. probl. mat.”, vol.2, M., 1973 (Russian). E. P. Cojuhari
  • Department of Mathematical Modelling and Economical Informatics, State University of Moldova, str. A. Mateevici 60, MD-2009, Chisinau, Moldova
  • E-mail: cojuhari@usm.md
There are 17 citations in total.

Details

Other ID JA46VR42GS
Journal Section Articles
Authors

E. P. Cojuhari This is me

Publication Date December 1, 2007
Published in Issue Year 2007 Volume: 2 Issue: 2

Cite

APA Cojuhari, E. P. (2007). MONOID ALGEBRAS OVER NON-COMMUTATIVE RINGS. International Electronic Journal of Algebra, 2(2), 25-53.
AMA Cojuhari EP. MONOID ALGEBRAS OVER NON-COMMUTATIVE RINGS. IEJA. December 2007;2(2):25-53.
Chicago Cojuhari, E. P. “MONOID ALGEBRAS OVER NON-COMMUTATIVE RINGS”. International Electronic Journal of Algebra 2, no. 2 (December 2007): 25-53.
EndNote Cojuhari EP (December 1, 2007) MONOID ALGEBRAS OVER NON-COMMUTATIVE RINGS. International Electronic Journal of Algebra 2 2 25–53.
IEEE E. P. Cojuhari, “MONOID ALGEBRAS OVER NON-COMMUTATIVE RINGS”, IEJA, vol. 2, no. 2, pp. 25–53, 2007.
ISNAD Cojuhari, E. P. “MONOID ALGEBRAS OVER NON-COMMUTATIVE RINGS”. International Electronic Journal of Algebra 2/2 (December 2007), 25-53.
JAMA Cojuhari EP. MONOID ALGEBRAS OVER NON-COMMUTATIVE RINGS. IEJA. 2007;2:25–53.
MLA Cojuhari, E. P. “MONOID ALGEBRAS OVER NON-COMMUTATIVE RINGS”. International Electronic Journal of Algebra, vol. 2, no. 2, 2007, pp. 25-53.
Vancouver Cojuhari EP. MONOID ALGEBRAS OVER NON-COMMUTATIVE RINGS. IEJA. 2007;2(2):25-53.