Ideal Generated

Some articles on ideal, ideal generated, ideals:

Discrete Valuation Ring - Examples
... The maximal ideal of Z(2) is the principal ideal generated by 2, and the "unique" irreducible element (up to units) is 2 ... Note that Z(2) is the localization of the Dedekind domain Z at the prime ideal generated by 2 ... of a Dedekind domain at a non-zero prime ideal is a discrete valuation ring in practice, this is frequently how discrete valuation rings arise ...
Euclidean Algorithm - Background — Greatest Common Divisor
... In modern mathematical language, the ideal generated by a and b is the ideal generated by g alone (an ideal generated by a single element is called a principal ideal, and all ideals ...
Hilbert Series And Hilbert Polynomial - Computation of Hilbert Series and Hilbert Polynomial
... Thus let K a field, be a polynomial ring and I be an ideal in R ... Let H be the homogeneous ideal generated by the homogeneous parts of highest degree of the elements of I ... total degree partial ordering and G the (homogeneous) ideal generated by the leading monomials of the elements of B ...
Irreducible Element
... Moreover, while an ideal generated by a prime element is a prime ideal, it is not true in general that an ideal generated by an irreducible element is an ... However, if is a GCD domain, and is an irreducible element of, then the ideal generated by is an irreducible ideal of ...

Famous quotes containing the words generated and/or ideal:

    “Here [in London, history] ... seemed the very fabric of things, as if the city were a single growth of stone and brick, uncounted strata of message and meaning, age upon age, generated over the centuries to the dictates of some now all-but-unreadable DNA of commerce and empire.”
    —William Gibson (b. 1948)

    “Every epoch which seeks renewal first projects its ideal into a human form. In order to comprehend its own essence tangibly, the spirit of the time chooses a human being as its prototype and raising this single individual, often one upon whom it has chanced to come, far beyond his measure, the spirit enthuses itself for its own enthusiasm.”
    —Stefan Zweig (18811942)