{"product_id":"computational-aspects-of-polynomial-identities-9781498720083","title":"Computational Aspects of Polynomial Identities","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cp\u003e\u003cstrong\u003eComputational Aspects of Polynomial Identities: Volume l, Kemer's Theorems, 2nd Edition\u003c\/strong\u003e presents the underlying ideas in recent polynomial identity (PI)-theory and demonstrates the validity of the proofs of PI-theorems. This edition gives all the details involved in Kemer's proof of Specht's conjecture for affine PI-algebras in characteristic 0.\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cp\u003e\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cp\u003eThe book first discusses the theory needed for Kemer's proof, including the featured role of Grassmann algebra and the translation to superalgebras. The authors develop Kemer polynomials for arbitrary varieties as tools for proving diverse theorems. They also lay the groundwork for analogous theorems that have recently been proved for Lie algebras and alternative algebras. They then describe counterexamples to Specht's conjecture in characteristic \u003ci\u003ep\u003c\/i\u003e as well as the underlying theory. The book also covers Noetherian PI-algebras, PoincaréHilbert series, GelfandKirillov dimension, the comb\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e\u003c\/p\u003e\u003cp\u003e\u003cstrong\u003eBasic Associative PI-Theory:\u003c\/strong\u003e\u003ci\u003e \u003c\/i\u003eBasic Results. A Few Words Concerning Affine PI-Algebras: Shirshov’s Theorem. Representations of \u003ci\u003eSn \u003c\/i\u003eand Their Applications.\u003cb\u003e Affine PI-Algebras:\u003ci\u003e \u003c\/i\u003e\u003c\/b\u003eThe Braun-Kemer-Razmyslov Theorem. Kemer’s Capelli Theorem.\u003cb\u003e Specht’s Conjecture:\u003ci\u003e \u003c\/i\u003e\u003c\/b\u003eSpecht’s Problem and Its Solution in the Affine Case (Characteristic 0). Superidentities and Kemer’s Solution for Non-Affine Algebras. Trace Identities. PI-Counterexamples in Characteristic \u003ci\u003ep\u003c\/i\u003e.\u003ci\u003e \u003c\/i\u003e\u003cb\u003eOther Results for Associative PI-Algebras:\u003ci\u003e \u003c\/i\u003e\u003c\/b\u003eRecent Structural Results. Poincaré-Hilbert Series and Gelfand-Kirillov Dimension. More Representation Theory.\u003cb\u003e Supplementary Material:\u003ci\u003e \u003c\/i\u003e\u003c\/b\u003eList of Theorems. Some Open Questions.\u003cb\u003e \u003c\/b\u003eBibliography.\u003c\/p\u003e","brand":"Taylor \u0026 Francis Inc","offers":[{"title":"Default Title","offer_id":49409281720663,"sku":"9781498720083","price":166.25,"currency_code":"GBP","in_stock":false}],"url":"https:\/\/bookcurl.com\/products\/computational-aspects-of-polynomial-identities-9781498720083","provider":"Book Curl","version":"1.0","type":"link"}