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1984•Bulletin of the Australian Mathematical SocietyOpen access

Does the Frobenius endomorphism always generate a direct summand in the endomorphism monoids of fields of prime characteristic?

Péter Pröhle

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Abstract

Letrbe a given prime. Then a monoidMis the endomorphism monoid of a field of characteristicrif and only if eitherMis a finite cyclic group orMis a right cancellative monoid andMhas an element of infinite order in its centre. The main lemma is the technical base of the present and other papers.

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Letrbe a given prime. Then a monoidMis the endomorphism monoid of a field of characteristicrif and only if eitherMis a finite cyclic group orMis a right cancellative monoid andMhas an element of infinite order in its centre. The main lemma is the technical base of the present and other papers.

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Available abstract

Letrbe a given prime. Then a monoidMis the endomorphism monoid of a field of characteristicrif and only if eitherMis a finite cyclic group orMis a right cancellative monoid andMhas an element of infinite order in its centre. The main lemma is the technical base of the present and other papers.

Key concepts: Endomorphism, Mathematics, Monoid, Prime (order theory), Lemma (botany), Pure mathematics, Element (criminal law), Order (exchange)

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