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der Universitat Munchen Set 11

Prof. Dr. B. Pareigis

Problem set for

Advanced Algebra

(41) LetK beaeld. Showthat(KK)-Modisnot equivalentto

K-Mod.

(42) Show that R-Mod6

=

C-Mod (not equivalent).

(43) Let K be a eld, B := M

n (K),

K P

B

:= K n

the set of row

vectors,

B Q

K

the set ofcolumnvectors. Findf :P

B

Q !K

and g : Q

K

P ! B, such that (K;B;P;Q;f;g) is a Morita

context. Is this a strict Morita context? Determine the center

of B and the set of twosided ideals of B.

(44) Determine the image of the maps f and g in the canonical

Morita context (A;B;P;Q;f;g) for

(a) A :=Z=(6)and P :=Z=(2),

(b) A :=Z=(4)and P :=Z=(4)Z=(2),

(c) A :=Z=(6)and P :=Z=(6)Z=(2).

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