By Dr. Otto Hesse

Leipzig 1872 zweite auflage, Teubner. In German. 8vo, 48pp., got rid of and rebound in later wrap with unique revealed yellow wraps certain in. modern college stamp and light-weight proprietor signature on entrance. stable plus.

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**Example text**

Suppose now that x is invertible. By no. 3, Corollary 2 to Proposition 4, n f ( n ) = T x is invertible for every integer n ^ 0. By construction, Z is the group of differences of N and hence (no. 4, Theorem 1 )f extends uniquely to a homo morphism g of Z into E. If g’ is a homomorphism of Z into E with £'(1) = x , the restriction f 'of g’ to N is a homomorphism of N into E with f ( 1) = x . Hence f = f , whence g = g. We shall apply Lemma 2 to the case where the monoid E is Z ; for every integer m e 2.

5) Given an action of fl on E with law denoted by I, a subset S of and a subset X of E, 8 ± X denotes the set of a ± x with a e S and * e X ; when 3 consists of a single element a, we generally write a I X instead of ( a } ± X. The mapping which associates with a e fl the mapping X i—>- a ± X is an action of Q on ^(E), which is said to be derh’ed irom the given action by ex tension to the set of subsets. (6) Let a h/, be an action of Q on E. Let g be a mapping of into Q. Then the mapping (3 •—i/(p) is an action of R' on E.

In this chapter we shall say, for the sake of abbreviation, "law of action" Or sometimes the external law

### Die Determinanten elementar behandelt by Dr. Otto Hesse

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