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Postulates for the Inverse Operations in a Group *
| Content Provider | Semantic Scholar |
|---|---|
| Copyright Year | 2010 |
| Abstract | It may happen that the function F is of such a character that when the ©-symbols z, x are given in (1), an ©-symbol y is uniquely determined, and when the©-symbols y, z are given in (1), an ©-symbol x is uniquely determined. In this case we may associate with the function F(x, y) two other one-valued functions y = G(z, x), x = H(y, z) defined over the collection®. These functions are called the first and second inverses of the function F. The primary object of this paper is to state the restrictions which must be imposed upon F in order that one of its inverses may define with © an abstract group. It is convenient, in developing the properties of the system {© ; o} consisting of the ©-symbols, F, and one or more postulates, to replace (1) by the notation f z = x o y. |
| File Format | PDF HTM / HTML |
| Alternate Webpage(s) | http://www.ams.org/journals/tran/1930-032-03/S0002-9947-1930-1501550-7/S0002-9947-1930-1501550-7.pdf |
| Language | English |
| Access Restriction | Open |
| Subject Keyword | Emoticon HL7PublishingSubSection |
| Content Type | Text |
| Resource Type | Article |
