MARC Record from marc_columbia

LEADER: 04689cam a2200589 i 4500
001 15625284
005 20210913163528.0
008 200504s2020 riua b 001 0 eng
010 $a 2020001994
035 $a(OCoLC)on1154985850
040 $aLBSOR/DLC$beng$erda$cDLC$dOCLCO$dOCLCF$dUAB$dOCLCO$dYDX$dOCLCO$dKSU$dVT2
020 $a9781470451745$qhardcover
020 $a1470451743$qhardcover
020 $z9781470456955$qelectronic book
035 $a(OCoLC)1154985850
042 $apcc
050 00 $aQA251.3$b.A42 2020
082 00 $a512/.4$223
084 $a16H05$a16R10$a16R20$a16R30$a16W22$a15A75$a15A72$a14L24$a16N60$a16P90$2msc
049 $aZCUA
100 1 $aAljadeff, Eli$q(Eliahu),$d1956-$eauthor.
245 10 $aRings with polynomial identities and finite dimensional representations of algebras /$cEli Aljadeff, Antonio Giambruno, Claudio Procesi, Amitai Regev.
264 1 $a[Providence, Rhode Island] :$bAmerican Mathematical Society,$c[2020]
300 $axii, 630 pages :$billustrations ;$c27 cm.
336 $atext$btxt$2rdacontent
337 $aunmediated$bn$2rdamedia
338 $avolume$bnc$2rdacarrier
490 1 $aAmerican Mathematical Society colloquium publications,$x0065-9258 ;$vvolume 66
504 $aIncludes bibliographical references (pages 605-621) and index.
505 0 $aNoncommutative algebra -- Universal algebra -- Symmetric functions and matrix invariants -- Polynomial maps -- Azumaya algebras and irreducible representations -- Tensor symmetry -- Growth -- Shirshov's height theorem -- 2 x 2 matrices -- Matrix identities -- Structure theorems -- Invariants and trace identities -- Involutions and matrices -- A geometric approach -- Spectrum and dimension -- The nilpotent radical -- Finite-dimensional and affine PI algebras -- The relatively free algebras -- Identities and superalgebras -- The Specht problem -- The PI-exponent -- Codimension growth for matrices -- Codimension growth for algebras satisfying a Capelli identity.
520 $aA 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 call a PI algebra, and this is the main object of study in this book, which can be used by graduate students and researchers alike.
650 0 $aPolynomial rings.
650 0 $aPI-algebras.
650 0 $aRepresentations of algebras.
650 7 $aPI-algebras.$2fast$0(OCoLC)fst01049848
650 7 $aPolynomial rings.$2fast$0(OCoLC)fst01070714
650 7 $aRepresentations of algebras.$2fast$0(OCoLC)fst01094934
650 7 $aAssociative rings and algebras {For the commutative case, see 13-XX} -- Algebras and orders {For arithmetic aspects, see 11R52, 11R54, 11S45; for representation theory, see 16G30} -- Separable algebra.$2msc
650 7 $aAssociative rings and algebras {For the commutative case, see 13-XX} -- Rings with polynomial identity -- $T$-ideals, identities, varieties of rings and algebras.$2msc
650 7 $aAssociative rings and algebras {For the commutative case, see 13-XX} -- Rings with polynomial identity -- Semiprime p.i. rings, rings embeddable in matrices over commutative rings.$2msc
650 7 $aAssociative rings and algebras {For the commutative case, see 13-XX} -- Rings with polynomial identity -- Trace rings and invariant theory.$2msc
650 7 $aAssociative rings and algebras {For the commutative case, see 13-XX} -- Rings and algebras with additional structure -- Actions of groups and semigroups; invariant theory.$2msc
650 7 $aLinear and multilinear algebra; matrix theory -- Basic linear algebra -- Exterior algebra, Grassmann algebras.$2msc
650 7 $aLinear and multilinear algebra; matrix theory -- Basic linear algebra -- Vector and tensor algebra, theory of invariants [See also 13A50, 14L24].$2msc
650 7 $aAlgebraic geometry -- Algebraic groups {For linear algebraic groups, see 20Gxx; for Lie algebras, see 17B45} -- Geometric invariant theory [See also 13A50].$2msc
650 7 $aAssociative rings and algebras {For the commutative case, see 13-XX} -- Radicals and radical properties of rings -- Prime and semiprime rings [See also 16D60, 16U10].$2msc
650 7 $aAssociative rings and algebras {For the commutative case, see 13-XX} -- Chain conditions, growth conditions, and other forms of finiteness -- Growth rate, Gelfand-Kirillov dimension.$2msc
700 1 $aGiambruno, A.,$eauthor.
700 1 $aProcesi, Claudio,$eauthor.
700 1 $aRegev, Amitai,$eauthor.
830 0 $aColloquium publications (American Mathematical Society) ;$vv. 66.
852 00 $bmat$hQA1$i.A5225 v.66