Sentence examples for left ideals from inspiring English sources

We use weak factorization of operators in the group von Neumann algebra VN(G×H) to prove that there exist at least 22b(G) left ideals of dimensions at least 22b(G) in A(G×H ∗∗ and in UC2(G×H)∗.

A semitopological semigroup S is left (respectively, right) reversible if any two closed right (respectively, left) ideals of S have nonvoid intersection, i.e., a S ¯ ∩ b S ¯ ≠ ∅ (respectively, S a ¯ ∩ S b ¯ ≠ ∅ ), for a, b ∈ S, where E ¯ denotes the closure of a set E in a topological space.

A semitopological semigroup S is said to be left (resp. right) reversible if any two closed right (resp. left) ideals of S have nonvoid intersection.

But most progressives backed World War II as a battle against the enemies of freedom, and their cherished causes of industrial unionism and racial tolerance gained as the fighting raged Now, though President Bush is a Republican, he is using words saturated with historic left ideals to win the confidence of many Americans.

In this case, must contain minimal left ideals.

G is called right reversible if any two closed left ideals of G have nonvoid intersection.

Definition 1 (Left Ideal).

Let ({mathcal A}) be a (mathbb {K} -algebra with a non-zero left ideal I of finite (mathbb K)-dimension.

The ring R is called purely infinite simple in case R is simple, and each nonzero left ideal of R contains an infinite idempotent.

Next we show that the only situation where algebraic amenability and proper algebraic amenability differ is when the (mathbb K -algebra contains a non-zero left ideal of finite (mathbb K -algebraon, as demonstrated by the following theorem.

It follows that (W_mathcal {F} = W_{mathcal {F}_1}) for any finite (mathcal {F} subset {mathcal A}) containing (mathcal {F}_1), and thus (a cdot W_{mathcal {F}_1} subseteq W_{mathcal {F}_1}) for any (a in {mathcal A}), i.e., (W_{mathcal {F}_1}) is a non-zero left ideal with finite (mathbb {K} -dimension.