Vol. 59, No. 1, 1975

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Adjunctions and comonads in differential algebra

William Francis Keigher

Vol. 59 (1975), No. 1, 99–112

It is known that the construction of the ring of fractions S1A of a commutative ring A by a multiplicative subset S of A can be extended to the differential case. This means that for a given differential ring (A,d), the differential ring of fractions of (A,d) by S is constructed simply by defining a derivation operator on S1A in terms of the derivation operator d on A. We seek to explain in the categorical setting of adiunctions and comonads the reasons for which this and other constructions can be extended to the differential case. A natural product of this investigation is the construction of the differential affine scheme of a differential ring.

Mathematical Subject Classification 2000
Primary: 12H05
Received: 22 August 1974
Revised: 20 February 1975
Published: 1 July 1975
William Francis Keigher