Annales Academić Scientiarum Fennicć
Mathematica
Volumen 32, 2007, 471-480

MULTIPLICATIVE BIJECTIONS BETWEEN ALGEBRAS OF DIFFERENTIABLE FUNCTIONS

Janez Mrcun and Peter Semrl

University of Ljubljana, Department of Mathematics
Jadranska 19, 1000 Ljubljana, Slovenia; janez.mrcun 'at' fmf.uni-lj.si

University of Ljubljana, Department of Mathematics
Jadranska 19, 1000 Ljubljana, Slovenia; peter.semrl 'at' fmf.uni-lj.si

Abstract. We show that any multiplicative bijection between the algebras of differentiable functions, defined on differentiable manifolds of positive dimension, is an algebra isomorphism, given by composition with a unique diffeomorphism.

2000 Mathematics Subject Classification: Primary 58A05; Secondary 46E25.

Key words: Differentiable functions, algebra isomorphisms, semigroup isomorphisms.

Reference to this article: J. Mrcun and P. Semrl: Multiplicative bijections between algebras of differentiable functions. Ann. Acad. Sci. Fenn. Math. 32 (2007), 471-480.

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