Yog tias A yog tus lej lej ntawm thaj chaw F, tom qab ntawd ib qho A-module yog ib txwm yog qhov chaw F-vector (ntawm lub nplhaib homomorphism F → A uas txhais cov qauv algebra ntawm A). Xws li ib qho qauv yog qhov ntev kawg yog tias nws qhov loj me raws li qhov chaw F-vector yog qhov kawg.
Af hauv lej yog dab tsi?
Nyob rau hauv lej, ib qho kwv yees finite-dimensional (AF) C-algebra yog C-algebra uas yog inductive txwv ntawm ib theem ntawm finite-dimensional C - algebras. Kwv yees li ntawm qhov kawg-dimensionality yog thawj zaug txhais thiab piav qhia txog kev sib txuas los ntawm Ola Bratteli.
Tus lej lej ntawm F yog dab tsi?
Hauv kev ua lej, tus lej lej hla ib thaj chaw (feem ntau hu ua tus lej lej) yog ib qhov chaw vector nruab nrog cov khoom lag luam bilinear … Ntau tus kws sau ntawv siv lo lus algebra los txhais tau tias associative algebra, lossis unital associative algebra, los yog hauv qee yam kev kawm xws li algebraic geometry, unital associative commutative algebra.
Dab tsi yog qhov loj me hauv linear algebra?
Ib qho txiaj ntsig tseem ceeb hauv linear algebra yog cov hauv qab no: Txhua lub hauv paus rau V muaj tib tus lej ntawm vectors Tus naj npawb ntawm vectors hauv lub hauv paus rau V yog hu ua qhov loj ntawm V, denoted by dim(V). Piv txwv li, qhov dimension ntawm Rn yog n. … Ib qhov chaw vector uas tsuas muaj pes tsawg vector muaj qhov loj me.
Dab tsi yog ib qho piv txwv algebra?
A unital algebra – an algebra that has a multiplicative identity element A geometric unital – a 2-(n3 + 1, n + 1, 1) block design for integer n ≥ 3. A unital algebraic structure, xws li unital magma. Daim ntawv qhia kev sib koom ua ke ntawm C -algebras - daim ntawv qhia uas khaws cov cim cim.
