Subfield-Compatible Polynomials over Finite Fields - Rose
... Gröbner bases to obtain unique representatives of polynomials that are equivalent on a set. Definition 2.6. A Gröbner basis for an ideal I in the polynomial ring E[x1 , . . . , xd ] is a finite set of generators {g1 , . . . , gm } for I whose leading terms generate the ideal of all leading terms i ...
... Gröbner bases to obtain unique representatives of polynomials that are equivalent on a set. Definition 2.6. A Gröbner basis for an ideal I in the polynomial ring E[x1 , . . . , xd ] is a finite set of generators {g1 , . . . , gm } for I whose leading terms generate the ideal of all leading terms i ...
Algebraic Groups
... The proof shows that R∗ is a special open set of R. In particular, R∗ is irreducible of dimension dim R∗ = dim R. 1.2. Isomorphisms and products. It follows from our definition that an algebraic group G is an affine variety with a group structure. These two structures are related in the usual way. N ...
... The proof shows that R∗ is a special open set of R. In particular, R∗ is irreducible of dimension dim R∗ = dim R. 1.2. Isomorphisms and products. It follows from our definition that an algebraic group G is an affine variety with a group structure. These two structures are related in the usual way. N ...