Content deleted Content added
grammar: "...take the ring to a particular..." -> "...take the ring to be a particular..." |
|||
Line 20:
# (''r''+''s'')''x'' = ''rx''+''sx''
# (''rs'')''x'' = ''r''(''sx'')
# 1''x'' = ''x'' (If R is a ring with unity)
Usually, we simply write "a left ''R''-module ''M''" or <sub>''R''</sub>''M''. A <b>right ''R''-module</b> ''M'' or ''M''<sub>''R''</sub> is defined similarly, only the ring acts on the right, i.e. we have a scalar multiplication of the form ''M'' × ''R'' → ''M'', and the above axioms are written with scalars ''r'' and ''s'' on the right of ''x'' and ''y''.
| |||