On N-Dimensional Achr-Algebras

  • Amir A. Mohammed University of Mosul
  • Abdulhakeem L. Hasan University of Mosul
Keywords: Automatic continuity, Finite-dimension, Homomorphism, Normed algebra


We prove that a homomorphismfrom complete normed algebra A into an n-dimensional normed algebra B is automatically continuous. As a consequence, B is ACHR-algebra.

Author Biographies

Amir A. Mohammed, University of Mosul

Department of Mathematics. College of Education. University of Mosul. Mosul. Iraq

Abdulhakeem L. Hasan, University of Mosul

Department of Mathematics. College of Education. University of Mosul. Mosul. Iraq


Bade, W.G., and Curtis Jr, P.C.(1978). Prime ideals and automatic continuity problems for Banach algebra. J. Funct. Anal, 29, 88-103.
Cedilnik, A., and Rodriguez, A.(2001). Automatic continuity of homomorphisms into normed quadratic algebras. Publ. Math. Debrecen ,59 (1–2), 79–88.
Cedilnik, A., and Rodriguez, A.(2003). Continuity of homomorphisms into complete normed algebraic algebras. J. Algebra, 264, 6–14.
Cedilnik, A.. Automatic continuity of homomorphisms into smooth normed algebras. Pre print 2013.
Dales, H. G.(1978) . Automatic continuity, a survey. Bull. London. Math. Soc, 10 , 129-183.
Palmer, T.W.(1994). Banach Algebras and the General Theory of -Algebras. vol. I, Algebras and Banach Algebras, Cambridge University Press, Cambridge.
Pfaffenberger, W. E., and Phillips, J.(1992). Commutative Gelfand theory for real Banach algebras. Representations as sections of bundles, Can. J. Math, 44, 342-356.
Rodriguez, A.(1983). Nonassociative normed algebras spanned by hermitian elements. Proc. London Math. Soc,47, 258-274.
Rodriguez, A.(1985). The uniqueness of the complete norm topology in complete normed nonassociative algebras. J. Funct. Anal, 60, 1-15.
Rodriguez, A.(1994). Nonassociative normed algebra. Geometric aspects, Banach Center Publications, Vol. 30, Institute of Mathematics, Polish Academy of Sciences, Warszawa , 299-311.
Rodriguez, A.(2000). Continuity of homomorphisms into normed algebras without topological divisors of zero. Rev. Real Acad. Cienc. Exact. Fis. Natur. Madrid, 94, 505–514.
Sinclair, A.M. (1976). Automatic continuity of linear operators, London Mathematical Society Lecture Note Series 21, Cambridge University Press, Cambridge.
How to Cite
Mohammed, A., & Hasan, A. (2013). On N-Dimensional Achr-Algebras. Science Journal of University of Zakho, 1(1), 333-337. Retrieved from https://sjuoz.uoz.edu.krd/index.php/sjuoz/article/view/106
Science Journal of University of Zakho