{"product_id":"separability-within-commutative-and-solvable-associative-algebras-under-consideration-of-non-unitary-algebras-with-401-exercises","title":"Separability within commutative and solvable associative algebras. Under consideration of non-unitary algebras. With 401 exercises","description":"\u003cp\u003eWithin the context of the Wedderburn-Malcev theorem a radical complement exists and all complements are conjugated. The main topics of this work are to analyze the Determination of a (all) radical complements, the representation of an element as the sum of a nilpotent and fully separable element and the compatibility of the Wedderburn-Malcev theorem with derived structures. Answers are presented in details for commutative and solvable associative algebras. Within the analysis the set of fully-separable elements and the generalized Jordan decomposition are of special interest. We provide examples based on generalized quaternion algebras, group algebras and algebras of traingular matrices over a field. The results (and also the theorem of Wedderburn-Malcev and Taft) are transferred to non-unitary algebras by using the star-composition and the adjunction of an unit. Within the App endix we present proofs for the Wedderburn-Malcev theorem for unitary algebras, for Taft's theorem on G-invariant radical complements for unitary algebras and for a theorem of Bauer concerning solvable unit groups of associative algebras.\u003c\/p\u003e\u003cdiv class=\"aw-variant-hidden-subtitle-div\" id=\"aw-variant-subtitle-9783960672210\"\u003e\u003ch3\u003e\u003c\/h3\u003e\u003c\/div\u003e","brand":"Libri","offers":[{"title":"Softcover - 9783960672210","offer_id":39445885878365,"sku":"9783960672210","price":49.99,"currency_code":"EUR","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0940\/0622\/files\/b1841746-9860-4086-90f8-abb657085281.jpg?v=1781240505","url":"https:\/\/shop.autorenwelt.de\/products\/separability-within-commutative-and-solvable-associative-algebras-under-consideration-of-non-unitary-algebras-with-401-exercises","provider":"Autorenwelt Shop","version":"1.0","type":"link"}