Triangular objects and systematic K-theory |
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Authors: | Thomas Hüttemann |
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Affiliation: | School of Mathematics and Physics, Pure Mathematics Research Centre, Queen’s University Belfast, Belfast, UK |
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Abstract: | We investigate modules over “systematic” rings. Such rings are “almost graded” and have appeared under various names in the literature; they are special cases of the G-systems of Grzeszczuk. We analyse their K-theory in the presence of conditions on the support, and explain how this generalises and unifies calculations of graded and filtered K-theory scattered in the literature. Our treatment makes systematic use of the formalism of idempotent completion and a theory of triangular objects in additive categories, leading to elementary and transparent proofs throughout. |
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Keywords: | Lower triangular category systematic ring systematic module Quillen K-theory |
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