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MONOID ALGEBRAS OVER NON-COMMUTATIVE RINGS

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

E. P. Cojuhari

https://izlik.org/JA82EX57HS

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

https://izlik.org/JA82EX57HS

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
Authors

E. P. Cojuhari This is me

Publication Date December 1, 2007
IZ https://izlik.org/JA82EX57HS
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. https://izlik.org/JA82EX57HS
AMA 1.Cojuhari EP. MONOID ALGEBRAS OVER NON-COMMUTATIVE RINGS. IEJA. 2007;2(2):25-53. https://izlik.org/JA82EX57HS
Chicago Cojuhari, E. P. 2007. “MONOID ALGEBRAS OVER NON-COMMUTATIVE RINGS”. International Electronic Journal of Algebra 2 (2): 25-53. https://izlik.org/JA82EX57HS.
EndNote Cojuhari EP (December 1, 2007) MONOID ALGEBRAS OVER NON-COMMUTATIVE RINGS. International Electronic Journal of Algebra 2 2 25–53.
IEEE [1]E. P. Cojuhari, “MONOID ALGEBRAS OVER NON-COMMUTATIVE RINGS”, IEJA, vol. 2, no. 2, pp. 25–53, Dec. 2007, [Online]. Available: https://izlik.org/JA82EX57HS
ISNAD Cojuhari, E. P. “MONOID ALGEBRAS OVER NON-COMMUTATIVE RINGS”. International Electronic Journal of Algebra 2/2 (December 1, 2007): 25-53. https://izlik.org/JA82EX57HS.
JAMA 1.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, Dec. 2007, pp. 25-53, https://izlik.org/JA82EX57HS.
Vancouver 1.E. P. Cojuhari. MONOID ALGEBRAS OVER NON-COMMUTATIVE RINGS. IEJA [Internet]. 2007 Dec. 1;2(2):25-53. Available from: https://izlik.org/JA82EX57HS