Vol. 61, No. 2, 1975

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Finitely generated ideals in regular F-algebras

James M. Briggs, Jr.

Vol. 61 (1975), No. 2, 339–350

Let A be a regular, semisimple, commutative F-algebra with identity. For each point in the spectrum of A, let 𝒜p denote the local algebra of germs at p of elements of A and let p denote its maximal ideal. When p is finitely generated we show to what extent representatives of its generators are generators of the maximal ideals in the algebras of functions locally belonging to A on some neighborhood of p. We show that if p is finitely generated, then all point derivations of A at p are continuous. Using this last fact, we describe the generators of maximal ideals when the polynomials in finitely many elements of the algebra are dense in the algebra.

Mathematical Subject Classification 2000
Primary: 46J20
Received: 27 August 1974
Published: 1 December 1975
James M. Briggs, Jr.