c.
For a module M of a ring R, any alternating map out of R to the n can be written as the composition of a map corresponding to this quantity and a linear map. That map corresponding to this quantity is sometimes denoted with a wedge symbol. An alternating map applied to n (*) vectors is equal to this quantity times that map evaluated at the basis vectors. This quantity is equal to the sum over all permutations sigma of the sign of sigma times the product of a sub i comma sigma i. This quantity is invariant under the transpose, and can be computed using expansion by minors. For 10 points, name this quantity that for the two by two matrix with entries a, b, c, d is equal to a times d minus b times c.
For a module M of a ring R, any alternating map out of R to the n can be written as the composition of a map corresponding to this quantity and a linear map.
determinant