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MATHEMATICA BOHEMICA, Vol. 127, No. 4, pp. 605-611 (2002)
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# The integrability of a field of endomorphisms

## Gerard Thompson

* Gerard Thompson*, Department of Mathematics, The University of Toledo, Toledo, Ohio 43606, U.S.A., e-mail: ` gthompson@uoft02.utoledo.edu`

**Abstract:**
A Theorem is proved that gives intrinsic necessary and sufficient conditions for the integrability of a zero-deformable field of endomorphisms. The Theorem is proved by reducing to a special case in which the endomorphism field is nilpotent. Many arguments used in the derivation of similar results are simplified, principally by means of using quotient rather than subspace constructions.

**Keywords:** integrability, endomorphism, quotient space

**Classification (MSC2000):** 53C10, 53C15, 53A35

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