I am now reading the book by Blyth, 'Module thery---an approach to linear algebra'.
I do not understand such a paragraph with which he motivates the learning of module theory:
In many ways, however, the notion of a vector space is too restrictive. Perhaps one way we can illustrate this is by asking the following question: has it occurred to the reader that, in most elementary introductions to linear algebra, determinants are defined for square matrices whose entries belong to a given field yet, come the consideration of eigenvalues, the matrix whose determinant has to be found has its entries in a polynomial ring? Put another way, should the various properties of determinants not really be developed in a more general setting?
Can anyone explain it in detail?