left module

left module

[′left ‚mäj·əl]
(mathematics)
A module over a ring in which the product of a member x of the module and a member a of the ring is written ax.
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.
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Recall from [Kle15] that a two-sided ideal J C A is an affine heredity ideal if; (SI1): [Hom.sub.A](J, A/J) = 0, (SI2): as a left module J [congruent to] m(q)P([pi]) for some graded multiplicity m(q) [member of] Z[q, [q.sup.-1]] and some [pi] [member of] [PI] such that [B.sub.[pi]] := [End.sub.A][(P([pi])).sup.op] [member of] B, and (PSI): as a right [B.sub.[pi]]-module P([pi]) is free finite rank.
In Figure 7(a), the left module structure had two wires on the middle position.
Let E be a left module over the algebra [L.sup.0](F, K) (briefly, an [L.sup.0](F, K)-module); the module multiplication [xi], x x is simply denoted by [[xi].sup.0] for any [xi] [member of] [L.sup.0](F, K) and x [member of] E.
He defines the C-completion C(M) and higher C-completions Cn(M) for an arbitrary left module M over a topological ring A.
The first left module is the PLL module which employed from Megawizard function in Altera [10].
The purpose of this paper is to describe a certain left module over Solomon's descent ring.
The upper left module, where one begins to read the work, is left untouched, but across the vast expanse of Rhapsody, as though it were an abstract comic strip of epic dimension, Bartlett has deployed a number of images.
For example, a left module over algebra A in tensor category [.sub.B][M.sub.B] is an A-B-bimodule N as an exercise in applying these ideas.
Obviously, for an F-measurable subset A of[OMEGA] and an [L.sup.0](F, K)-module S, [[??].sub.A]S := {[??].sub.A]x | x [member of] S), called the A-stratification of S, is a left module over the algebra [[??].sub.A] [L.sup.0](F, K) :={[??].sub.A.[epsilon] | [epsilon] [member of] [L.sup.0](F,K)} and ([L.sup.p]([[??].sub.A]S), [parallel]* [parallel]p) is an ordinary Banach space.
For the product, Theorem 4.1, using the left module coalgebra action defined in Lemma 4.6, gives
A left module over a topological algebra A which is a tvs with separately continuous outer multiplication is called topological left A-module.
Is there any relations between the two monoidal categories [.sub.H]M and [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] of left modules over two cocycle twist-equivalent Hopf algebras H and [H.sup.[sigma]]?