Module contractibility for semigroup algebras

Document Type: Research Articles

Author

Department of Mathematics, Islamic Azad University, Garmsar Branch, Garmsar, Iran.

Abstract

In this paper, we nd the relationships between module contractibility of a
Banach algebra and its ideals. We also prove that module contractibility of
a Banach algebra is equivalent to module contractibility of its module uniti-
zation. Finally, we show that when a maximal group homomorphic image of
an inverse semigroup S with the set of idempotents E is nite, the module
projective tensor product l1(S)×l1(E)l1(S) is l1(E)-module contractible.

[1] M. Amini, Module amenability for semigroup algebras, Semigroup Forum,
69 (2004), 243{254.
[2] M. Amini, A. Bodaghi and D. Ebrahimi Bagha, Module amenability of
the second dual and module topological center of semigroup algebras,
Semigroup Forum, 80 (2010), 302{312.
[3] A. Bodaghi, Module amenability and tensor product of semigroup
algebras, J. Math. Extension, 4 (2010), 97{106.
[4] A. Bodaghi, The structure of module contractible Banach algebras, Int.
J. Nonlinear Anal., 1 (2010), 6{11.
[5] A. Bodaghi, Module amenability of the projective module tensor product,
Malaysian J. Math. Sci., 5 (2011), 257{265.

[6] H. G. Dales, Banach Algebras and Automatic Continuity, Oxford
University Press, Oxford, 2000.
[7] J. Duncan, I. Namioka, Amenability of inverse semigroups and their
semigroup algebras, Proc. Roy. Soc. Edinburgh, 80 (1988), 309-321.
[8] G. H. Esslamzadeh and T. Esslamzadeh, Contractability of `1-Munn
Algebras with Applications, Semigroup Forum, 63 (2001), 1{10.
[9] N. Grnbk, Amenability of weighted discrete convolution algebras on
cancellative semigroups, Proc. Roy. Soc. Edinburgh, 110 (1998), 351{360.
[10] B. E. Johnson, Cohomology in Banach algebras, Memoirs Amer. Math.
Soc. 127, Amer. Math. Soc., Providence, 1972.
[11] W.D. Munn, A class of irreducible matrix representations of an arbitrary
inverse semigroup, Proc. Glasgow Math. Assoc., 5 (1961), 41{48.
[12] H. Pourmahmood-Aghababa, (Super) module amenability, module
topological centre and semigroup algebras, Semigroup Forum, 81 (2010),
344{356.
[13] H. Pourmahmood-Aghababa, A note on two equivalence relations on
inverse semigroups, Semigroup Forum, DOI 10.1007/s00233-011-
9365-z.
[14] R. Rezavand, M. Amini, M. H. Sattari, and D. Ebrahimi Bagha, Module
Arens regularity for semigroup algebras, Semigroup Forum, 77 (2008),
300{305.
[15] V. Runde, Lectures on Amenability, Lecture Notes in Mathematics 1774,
Springer-Verlag, Berlin-Heidelberg-New York, 2002.
[16] Yu. V. Selivanov, Banach algebras of small global dimension zero, Uspekhi
Mat. Nauk., 31 (1976), 227{228.