Sentence examples for distinguished element from inspiring English sources

As the V -monoid of a ring, M is of course conical, and contains a distinguished element (as described prior to Theorem 2).

(Bergman's Theorem) [49, Theorem 6.2] Let M be a finitely generated commutative conical monoid with distinguished element d ≠ 0, and let K be any field.

Now denote by ({text {Sets}}_+) the category of pointed sets, and consider the forgetful functor ({text {Ab}}rightarrow {text {Sets}}_+) sending an abelian group E to its underlying set with distinguished element (0 in E).

Let (Delta _+^flat = Delta _+ times _Delta Delta ^flat ), and note that the embedding (lambda :Delta rightarrow Delta _+) extends to an embedding begin{aligned} lambda ^flat :Delta ^flat rightarrow Delta _+^flat end{aligned} (6.22 that adds a new initial element to an ordinal [n], but keeps the same distinguished element l.

First, V ( R ) is conical: if x, y ∈ V ( R ) have x ⊕ y = 0, then x = y = 0. Second (for R unital), V ( R ) contains a distinguished element d : for each x ∈ V ( R ), there exists y ∈ V ( R ) and n ∈ N having x ⊕ y = n d (specifically, d = [ R ] ).

This functor has a left-adjoint sending a pointed set (langle X,o rangle ) to the quotient (mathsf{Span}(X) = {mathbb {Z}}[X]/{mathbb {Z}}cdot o) of the free abelian group ({mathbb {Z}}[X]) generated by X by the subgroup spanned by the distinguished element (o in X).

A structure for the language of equality consists simply of a non-empty universe of discourse; there are no relations or functions or distinguished elements.

Instead, as we have shown, determinate isotopic labeling states are distinguished elements of a multi-valued logic, whose undistinguished elements are identified with contradiction (bot) and the indeterminate isotopic labeling state (top).

Even on AAC-encoded tracks, I was able to distinguish elements of songs that I had never noticed before.

Everyone can smell everything I can smell, but they don't know how to understand it, distinguish elements, or how to speak about it.

Fans of the Weather Channel are no doubt familiar with ground clutter, a radar phenomenon in which buildings, hills and other fixed elements of the landscape return signals that can make it difficult to distinguish elements that weather radar is designed to see, like an approaching storm.