How to make many-sorted algebras one-sorted

Barry J. Gardner

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Generalization of the concept of variety and quasivariety to partial algebras through category theory

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CONTENTSIntroduction ................................................................................................5§1. The purely category theoretical version of Birkhoff's theorem................7§2. Category theoretical study of generalized identities............................19§3. Generalized identities in partial algebras.............................................29§4. Calculus...............................................................................................41§5....

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Using derived categories, we develop an alternative approach to defining Koszulness for positively graded algebras where the degree zero part is not necessarily semisimple.

Morphisms in the category of finite-dimensional absolute valued algebras

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This is a study of morphisms in the category of finite-dimensional absolute valued algebras whose codomains have dimension four. We begin by citing and transferring a classification of an equivalent category. Thereafter, we give a complete description of morphisms from one-dimensional algebras, partly via solutions of real polynomials, and a complete, explicit description of morphisms from two-dimensional algebras. We then give an account of the reducibility of the morphisms, and for...