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Let (K,|·|) be a complete non-Archimedean valuated field, with valuation ring R, and let f(X) be a power series with coefficients in R. Suppose at least one of the ...

A constant function is function f(x)=c whose value does not change as its parameters vary. The function graph of a one-dimensional constant function is a straight line. The ...

The dual vector space to a real vector space V is the vector space of linear functions f:V->R, denoted V^*. In the dual of a complex vector space, the linear functions take ...

For a diagonal metric tensor g_(ij)=g_(ii)delta_(ij), where delta_(ij) is the Kronecker delta, the scale factor for a parametrization x_1=f_1(q_1,q_2,...,q_n), ...

An additive group is a group where the operation is called addition and is denoted +. In an additive group, the identity element is called zero, and the inverse of the ...

An element a of a ring which is nonzero, not a unit, and whose only divisors are the trivial ones (i.e., the units and the products ua, where u is a unit). Equivalently, an ...

Given a module M over a commutative unit ring R and a filtration F:... subset= I_2 subset= I_1 subset= I_0=R (1) of ideals of R, the associated graded module of M with ...

Given a group G, the algebra CG is a vector space CG={suma_ig_i|a_i in C,g_i in G} of finite sums of elements of G, with multiplication defined by g·h=gh, the group ...

Given a module M over a commutative unit ring R and a filtration F:... subset= I_2 subset= I_1 subset= I_0=R (1) of ideals of R, the Rees module of M with respect to F is ...

A module M over a unit ring R is called faithful if for all distinct elements a, b of R, there exists x in M such that ax!=bx. In other words, the multiplications by a and by ...