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M with a submodule N, the module M is said to be an essential extension of N (or N is said to be an essential submodule or large submodule of M) if for...

also belong to ⁠ I {\displaystyle I} ⁠. (Equivalently, if it is a graded submodule of ⁠ R {\displaystyle R} ⁠; see § Graded module.) The intersection of...

photometry submodule of 7 bands (NUV, u, g, r, i, z, y) and the slitless spectroscopy submodule of 3 bands (GU, GV, GI). The multi-color photometry submodule includes...

outline of a proof: Denote by tM the torsion submodule of M. Torsion module can be embedded as a submodule of M and this gives short exact sequence: 0...

stating that every submodule of a finitely generated module over a Noetherian ring is a finite intersection of primary submodules. This contains the case...

Specifically, if Q is a submodule of some other module, then it is already a direct summand of that module; also, given a submodule of a module Y, any module...

injective module B, then E(M) is (isomorphic to) a submodule of B. If N is an essential submodule of M, then E(N)=E(M). Every module M has an injective...

modules into a new, larger module. The direct sum of modules is the smallest module which contains the given modules as submodules with no "unnecessary"...

non-zero submodules. 3.  An ideal or submodule is called irreducible if it cannot be written as an intersection of two larger ideals or submodules. If the...

unit and the valve. Secondly, the submodule capacitors themselves are large and bulky. A MMC is considerably larger than a comparable-rated 2-level converter...

Over a principal ideal domain (e.g., Z {\displaystyle \mathbb {Z} } ), a submodule of a free module is free. If R is commutative, the polynomial ring R [...

is in ⁠ I {\displaystyle I} ⁠. In other words, a left ideal is a left submodule of R, considered as a left module over itself. A right ideal is defined...

visualizations. CARTO is an active contributor to deck.gl and maintains a CARTO submodule inside deck.gl that allows developers to build their own applications...

An intuitive characterization of the lemma involves the notion that a submodule N of a module M over some ring A with specified ideal I holds a priori...

completely reducible) if it is the direct sum of simple (irreducible) submodules. A ring is said to be (left)-semisimple if it is semisimple as a left...

order of the factors. (M2) The torsion submodule is a direct summand. That is, there exists a complementary submodule P {\displaystyle P} of M {\displaystyle...

subrepresentation, such that the inertia group acts in a certain way on the submodule and the quotient. The exact condition depends on the author; for example...

M additively. Given such a G-module M, it is natural to consider the submodule of G-invariant elements: M G = { x ∈ M   |   ∀ g ∈ G :   g x = x } . {\displaystyle...

p(A)} . K r ( A , b ) {\displaystyle {\mathcal {K}}_{r}(A,b)} is a cyclic submodule generated by b {\displaystyle b} of the torsion k [ x ] {\displaystyle...

two-level converter submodules, i.e., a modular multilevel converter (MMC) scheme with a large step size, in which each half-bridge submodule contains several...