then Aa zB - GitHub Pages · nm 10h N Saen E Is L. Is our commotterys R nano s s miff MasN in R mad T if R is commutate M au R med can define an R R b mad stneeheanM by m r nm r m
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If A B are commutative R algebras
then Aa zB is the categoval sumf Ad B
i e tlom.p.algfAQBD tlomar.ayCA.dk
can HompalglB ccom
Monegenerally if A.Bnotnesc.commotte
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are a I
AaB seBu A
e
a b HalgCb e fog D
Adjointness of a sinestratnfsaksR 45 N an R module
L an S module
Dd yl L thought I as an R maddens'sX
Hom z N.ph HomslSqzN.L
HompCN xL s HomsCSaN L
N Sqn Ln 7 Ian
Thinkgren g N L III Saf L
suchthat diagram comatesnm 10h
N Saen EIs L
Is our commotterys
R nanos s
miff
MasNin R mad T
if R iscommutate M au R med
can define an R R bmad stneeheanM
by m r nm r m r m
rLmr r r'm r nm
Crm r
M N RMads can console hath as1212 binds
d argues another R R bmed
R mad
r man I r m an m ran man
manor
Digression
runletif he afull ofcharatiste 2
Let ULFbe avectorspace and consider
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Vat a q get vav F
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Claim if be Billu Z b b suchthat
b is skew symmetricb is symmetric
b b th
let on BillvBike defedby
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Define a hem fangs FEDEnd BillD
F algebrasx or
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b b'tb D to b d syn
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if d is slow dsymmor'd D 20 0
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Def If U a uspa elfdivisionring
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independent if Egaisio si
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Det s is a basis if it is an independent
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Prope If S is a spanningsetsuchthat no
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Proveit yourself orwilldiscuss later
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