{"product_id":"rings-with-polynomial-identities-and-finite-dimensional-representations-of-algebras-9781470451745","title":"Rings with Polynomial Identities and Finite","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eA polynomial identity for an algebra (or a ring) $A$ is a polynomial in noncommutative variables that vanishes under any evaluation in $A$. An algebra satisfying a nontrivial polynomial identity is called a PI algebra, and this is the main object of study in this book, which can be used by graduate students and researchers alike.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e\u003cul\u003e\n\u003cli\u003eIntroduction\u003c\/li\u003e\n\u003cli\u003eFoundations: Noncommutative algebra\u003c\/li\u003e\n\u003cli\u003eUniversal algebra\u003c\/li\u003e\n\u003cli\u003eSymmetric functions and matrix invariants\u003c\/li\u003e\n\u003cli\u003ePolynomial maps\u003c\/li\u003e\n\u003cli\u003eAzumaya algebras and irreducible representations\u003c\/li\u003e\n\u003cli\u003eTensor symmetry\u003c\/li\u003e\n\u003cli\u003eCombinatorial aspects of polynomial identities: Growth\u003c\/li\u003e\n\u003cli\u003eShirshov's theorem\u003c\/li\u003e\n\u003cli\u003e$2\\times2$ matrices\u003c\/li\u003e\n\u003cli\u003eThe structure theorems\u003c\/li\u003e\n\u003cli\u003eMatrix identities\u003c\/li\u003e\n\u003cli\u003eStructure theorems\u003c\/li\u003e\n\u003cli\u003eInvariants and trace identities\u003c\/li\u003e\n\u003cli\u003eInvolutions and matrices\u003c\/li\u003e\n\u003cli\u003eA geometric approach\u003c\/li\u003e\n\u003cli\u003eSpectrum and dimension\u003c\/li\u003e\n\u003cli\u003eThe relatively free algebras: The nilpotent radical\u003c\/li\u003e\n\u003cli\u003eFinite-dimensional and affine PI algebras\u003c\/li\u003e\n\u003cli\u003eThe relatively free algebras\u003c\/li\u003e\n\u003cli\u003eIdentities and superalgebras\u003c\/li\u003e\n\u003cli\u003eThe Specht problem\u003c\/li\u003e\n\u003cli\u003eThe PI-exponent\u003c\/li\u003e\n\u003cli\u003eCodimension growth for matrices\u003c\/li\u003e\n\u003cli\u003eCodimension growth for algebras satisfying a Capelli identity\u003c\/li\u003e\n\u003cli\u003eThe Golod-Shafarevich counterexamples\u003c\/li\u003e\n\u003cli\u003eBibliography\u003c\/li\u003e\n\u003cli\u003eIndex\u003c\/li\u003e\n\u003cli\u003eIndex of Symbols.\u003c\/li\u003e\n\u003c\/ul\u003e","brand":"MP-AMM American Mathematical","offers":[{"title":"Default Title","offer_id":50046686855511,"sku":"9781470451745","price":78.3,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9781470451745.jpg?v=1740272206","url":"https:\/\/bookcurl.com\/products\/rings-with-polynomial-identities-and-finite-dimensional-representations-of-algebras-9781470451745","provider":"Book Curl","version":"1.0","type":"link"}