Sentence examples for be a left module from inspiring English sources

Let E be a left module over the algebra L 0 ( F, K ).

Let E be a left module over the algebra (L^{0}(mathcal{F}, K)).

Let E be a left module over the algebra (L^{0}(mathcal{F})).

Let E be a left module over the algebra (L^{0}({mathcal {F}}, K)), a module homomorphism (f:Erightarrow L^{0}({mathcal {F}}, K)) is called an (L^{0}) (or (L^{0}({mathcal {F}}, K)))-linear function.

Let E be a left module over the algebra (L^{0}({mathcal {F}},R)), (Msubset E) be an (L^{0}({mathcal {F}},R -submodule,R -submoduleow L^{0}({mathcal {f}},R)) be an (L^{0})-linear function and (p:Erightarrow L^{0}({Mrightarrow},R)) be an (L^{0})-sublinear function such that (f(x)leq p(x),forall xin M).

Let E be a left module over the algebra L 0 ( F, R ), f : E → L 0 ( F, R ) a random linear functional and p : E → L 0 ( F, R ) an L 0 -linear function such that f ( x ) ≤ p ( x ), ∀ x ∈ E. Then f is an L 0 -linear function.

Furthermore, if, in addition, E is a left module over the algebra L 0 ( F, K ) (briefly, an L 0 ( F, K ) -module) such that.

Lemma 2.13 Suppose A is an A ∞ algebra and denote A regarded as a right module over itself as A r. Let P be a left A module, then the vector space A r ⊗ ∞ P is naturally quasi-isomorphic to H ∗ (P ).

Assume that is a left -module and is a left Banach -module.

Let (mathcal {R}) be a ring, (mathcal {X}) be a left (mathcal {R} -module, and (delta : mathcal {R} -moduleand{X}) be a left deltaation.

If (Phi _2) is a left A-module, and (Phi _1) is an A-bimodule, then the left module (Phi _1otimes Phi _2) is defined in the same way.