I am reading Professor Sturmfels's article What Is...a Gröbner Basis? In the definition of reduced Gröbner basis, I met a term trailing term of a polynomial. I do not konw what does it exactly mean. Can anyone give me some detail? Thanks in advance.
Trailing term, in this context, means any term except the leading term (with respect to the chosen admissable ordering). Condition (3) says that to turn a Gröbner basis into a reduced Gröbner basis you also have to cancel all terms in all elements of the Gröbner basis (by subtracting a suitable multiple of one of the other elements) when possible (i.e., if it indeed is a multiple of the leading term of one of the other elements).