Sentence examples for principal ideals from inspiring English sources

As an approach to governance, the principal ideals of civic republicanism can be traced back to the ancient works of Plato, Aristotle, Plutarch, and Cicero, among others; its more modern adherents include Niccolò Machiavelli, Montesquieu, James Harrington, and James Madison.

In the following, we discuss the relation between principal derivations and principal ideals in lattices.

By analogy with principal ideals, we introduce a principal derivation in lattices as follows.

In the following, we give a property of principal ideals in a modular lattice.

For X of arbitrary dimension, principal ideals are identified which are the building blocks for all other ideals.

Though most of the conventional error-correcting codes are principal ideals in the factor ring of a polynomial ring in one indeterminate.

(1) If d is a principal derivation of L, then Fix d ( L ) = I d is a principal ideal.

Proposition 4.7 In a modular lattice, every principal ideal is a semi-standard ideal.

If L satisfies A.C.C., then every ideal of L is a principal ideal.

If d is a principal derivation of L, then Fix d ( L ) = I d is a principal ideal.

Our theory is effective and yields an extension of Buchberger's algorithm to principal ideal rings.