Annals of Functional Analysis

On splitting of extensions of rings and topological rings

Mart Abel

Full-text: Open access


Several results on splitting of extensions of Banach algebras are generalized to the case of (not necessarily commutative, not necessarily unital) rings or topological rings. Detailed proofs of the results are provided.

Article information

Ann. Funct. Anal., Volume 1, Number 1 (2010), 123-132.

First available in Project Euclid: 12 May 2014

Permanent link to this document

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 16S70: Extensions of rings by ideals
Secondary: 16W80: Topological and ordered rings and modules [See also 06F25, 13Jxx] 46H99: None of the above, but in this section 54H13: Topological fields, rings, etc. [See also 12Jxx] {For algebraic aspects, see 13Jxx, 16W80}

Ring topological ring extension of a ring splitting


Abel, Mart. On splitting of extensions of rings and topological rings. Ann. Funct. Anal. 1 (2010), no. 1, 123--132. doi:10.15352/afa/1399900998.

Export citation


  • W.G. Bade, H.G. Dales and Z.A. Lykova, Algebraic and Strong Splittings of Extensions of Banach Algebras. Mem. Amer. Math. Soc. 137 (1999), no. 656.
  • H.G. Dales, Banach Algebras and Automatic Continuity. London Mathematical Society Monographs. New Series 24. Oxford Science Publications. The Clarendon Press, Oxford University Press, New York, 2000.
  • I.N. Herstein, Noncommutative Rings. Reprint of the 1968 original. With an afterword by Lance W. Small. Carus Mathematical Monographs, 15, Mathematical Association of America, 2005.
  • M.S. Monfared, Extensions and isomorphisms for the generalized Fourier algebras of a locally compact group. J. Funct. Anal. 198 (2003), no. 2, 413–444.
  • T.W. Palmer, Banach Algebras and the General Theory of $*$-algebras. Vol. I. Algebras and Banach Algebras. Encyclopedia of Mathematics and its Applications 49, Cambridge University Press, Cambridge, 1994.
  • J.S. Rose, On the splitting of extensions by a group of prime order. Math. Z. bf 117 1970, 239–248.
  • D.I. Zaitsev, Splittable extensions of abelian groups. (Russian) The structure of groups and the properties of their subgroups (Russian), 22–31, i, Akad. Nauk Ukrain. SSR, Inst. Mat., Kiev, 1986.