equivalent ring characteristic ''n'' '''z''' ''n'''''z''' algebra way given ''r'' module ''m'' endomorphism ring ''m'' denoted end sub ''r'' sub ''m'' ''r'' algebra defining ''r'' ''x'' ''r'' ''x'' ring matrices coefficients commutative ring ''r'' forms ''r'' algebra matrix addition multiplication coincides previous example ''m'' finitely generated free ''r'' module particular square ''n'' ''n'' matrices entries field ''k'' form associative algebra ''k'' complex numbers form dimensional commutative algebra real numbers quaternions form dimensional associative
Formal science Mathematics Pure mathematics Algebra Associative algebra