quotient module造句

• This quotient module is isomorphic to the complex numbers, viewed as a module over the real numbers "'R " '.
• Then R癏 is a right ideal and coideal in H, and the quotient module V = H / R癏 is a right H-module coalgebra.
• By extension, in abstract algebra, the term quotient space may be used for quotient modules, quotient rings, quotient groups, or any quotient algebra.
• For example, all subspaces of a Noetherian space, are Noetherian themselves; all subgroups and quotient groups of a Noetherian group are likewise, Noetherian; and, " mutatis mutandis ", the same holds for submodules and quotient modules of a Noetherian module.
• As a consequence, the depth of R in H is finite if and only if its " generalized quotient module " V represents an algebraic element in the representation ring ( or Green ring ) of R . This is the case for example if V is a projective module, or if V is a permutation module over a group algebra R ( i . e ., V has a basis that is a G-set ).