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Show that Mod-A and Mod-B are alsoequivalent

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(1)

der Universitat Munchen Set 12

Prof. Dr. B. Pareigis

Problem set for

Advanced Algebra

(45) (a) Let A-Mod be equivalent to B-Mod. Show that Mod-A

and Mod-B are alsoequivalent.

(b) Let K be an integral domain (commutative without zero-

divisors). Showthat K-Mod'Mod-K.

(46) Showthatanequivalenceofarbitrarycategoriespreservesmonomor-

phisms.

(47) Show that an equivalence of module categories preserves pro-

jective modules,but not free modules.

(48) Let D be a division algebra. Show that D-Mod ' Mod-D if

and onlyif there is anisomorphism of algebrasD

= D

op

.

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