Content deleted Content added
expanding article |
→Associated polynomials: divisibility |
||
Line 31:
are ''q - associates'' (note: the exponents "''q''<sup>''i''</sup> " of ''L''(''x'') have been replaced by "''i''" in ''l''(''x'')). More specifically, ''l(x}'' is called the ''conventional q-associate'' of ''L(x)'', and ''L(x)'' is the ''linearised q-associate'' of ''l(x)''.
If ''L''<sub>1</sub>(''x'') and ''L''<sub>2</sub>(''x'') are linearised polynomials over '''F'''<sub>''q''</sub> with conventional q-associates ''l''<sub>1</sub>(''x'') and ''l''<sub>2</sub>(''x'') respectively, then ''L''<sub>1</sub>(''x'') symbolically divides ''L''<sub>2</sub>(''x'') if and only if ''l''<sub>1</sub>(''x'') divides ''l''<sub>2</sub>(''x'').<ref>{{harvnb|Lidl|Niederreiter|1983|loc=pg. 115 (first edition) Corollary 3.60}}</ref> Furthermore,
''L''<sub>1</sub>(''x'') divides ''L''<sub>2</sub>(''x'') in the ordinary sense in this case.<ref>{{harvnb|Lidl|Neiderreiter|1983|loc=pg. 116 (first edition) Theorem 3.62}}</ref>
==Notes==
| |||