Term additive K-theory is a synonym for cyclic homology, used in early articles mainly of Russian and a bit by French school.
Additive K-theory is also a title of a historical article
Boris Tsygan, Boris Feigin, Additive K-theory, in K-theory, arithmetic and geometry, LNM 1289 (1987), edited by Yu. I. Manin, pp. 67–209, seminar 1984-1986 in Moscow), MR89a:18017
The additive K-theory is here studied in relation to the algebraic K-theory and Hochschild homology. Like there is a K-theory spectrum, one also constructs an additive K-theory/cyclic homology spectrum.
Contents of Tsygan-Feigin
Ch. 1. Additive K-functors.
Ch. 2. Derived functors and relative additive K-functors.
Ch. 3. Generalized free products.
Ch. A. Lie algebra homology.
Ch. 5. Operations in additive K-theory.
Ch. 6. Additive K-functors of the commutative noetherian algebras.
Ch. 7. Characteristic classes.
Appendix. Cyclic objects.
There is also the related article
Б. Л. Фейгин, Б. Л. Цыган, “Аддитивная K-теория и кристальные когомологии”, Функц. анализ и его прил., 19:2 (1985), 52–-62, pdf, MR88e:18008; Engl. transl. in B. L. Feĭgin, B. L. Tsygan, Additive -theory and crystalline cohomology, Functional Analysis and Its Applications, 1985, 19:2, 124–132.
Revised on December 2, 2010 19:35:01
by Zoran Škoda