Term additive K-theory is a synonym for cyclic homology, used in early articles mainly of Russian and a bit by French school. Sometimes, additive K-theory denotes more specifially a different packing of cyclic homology, namely with appropriately shifted degrees (see the reference by Loday-Quillen at Loday-Quillen-Tsygan theorem and the article by Kuribayashi below).
Additive K-theory is also a title of a historical article
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
Related articles include
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 $K$-theory and crystalline cohomology, Functional Analysis and Its Applications, 1985, 19:2, 124–132.
Katsuhiko Kuribayashi, Toshihiro Yamaguchi, On additive K-theory with the Loday-Quillen $\ast$-product, Math. Scand. 87, No 1 (2000) article doi
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