On Centralizing and Strong Commutativity Preserving Maps of Semiprime Rings

We study some properties of centralizing and strong commutativity preserving maps of semiprime rings.Вивчаються деякi властивостi централiзуючих та сильних вiдображень напiвпростих кiлець, що зберiгають комутативнiсть

Commutativity

We describe a general framework for notions of commutativity based on enriched category theory. We extend Eilenberg and Kelly's tensor product for categories enriched over a symmetric monoidal base to a tensor product for categories enriched over a normal duoidal category; using this, we re-find notions such as the commutativity of a finitary algebraic theory or a strong monad, the commuting tensor product of two theories, and the Boardman-Vogt tensor product of symmetric operads.Comment: 48 pages; final journal versio