### Some articles on *ideal, ideal generated, ideals*:

Discrete Valuation Ring - Examples

... The maximal

... 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

... 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

... 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

... 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)

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