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theory and module theory, each right (resp. left) R-module M has a singular submodule consisting of elements whose annihilators are essential right (resp
Singular_submodule
associative algebra that is a simple ring. singular submodule The right (resp. left) R-module M has a singular submodule if it consists of elements whose annihilators
Glossary_of_ring_theory
Branch of mathematics that studies algebraic structures
Annihilator (ring theory) Submodule Pure submodule Module homomorphism Essential submodule Superfluous submodule Singular submodule Socle of a module Radical
List of abstract algebra topics
List_of_abstract_algebra_topics
Type of algebraic structure
also belong to I {\displaystyle I} . (Equivalently, if it is a graded submodule of R {\displaystyle R} ; see § Graded module.) The intersection of
Graded_ring
Cohomology theory for topological spaces
) {\displaystyle C^{p}(X)} consisting of locally zero functions is a submodule, denote by C 0 p ( X ) {\displaystyle C_{0}^{p}(X)} . C 0 ∗ ( X ) = {
Alexander–Spanier_cohomology
Algebra describing 2D conformal symmetry
Verma module by its maximal submodule. A Verma module is irreducible if and only if it has no singular vectors. A singular vector or null vector of a highest
Virasoro_algebra
residue field. essential 1. A submodule M of N is called an essential submodule if it intersects every nonzero submodule of N. 2. An essential extension
Glossary of commutative algebra
Glossary_of_commutative_algebra
Algebra with unique prime factorization
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
Dedekind_domain
Tools for studying groups based on techniques from algebraic topology
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
Group_cohomology
On polynomial rings over fields
instance of the theorem asserting that over a principal ideal ring, every submodule of a free module is itself free. The Koszul complex, also called "complex
Hilbert's_syzygy_theorem
Representation of a quantum group
(L,B)} , such that L {\displaystyle L} is a free A {\displaystyle A} -submodule of M {\displaystyle M} such that M = Q ( q ) ⊗ A L ; {\displaystyle M=\mathbb
Crystal_base
Geometric arrangements of points, foundational to Lie theory
y\rangle } is preserved. The root lattice of a root system Φ is the Z-submodule of E generated by Φ. It is a lattice in E. The group of isometries of E
Root_system
Branch of mathematics
principal ideal domain. In particular, over a principal ideal domain, every submodule of a free module is free, and the fundamental theorem of finitely generated
Linear_algebra
Algebraic structure
for the divisor class of d. If F , F ′ {\displaystyle F,F'} are maximal submodules of M, then c ( χ ( M / F ) ) = c ( χ ( M / F ′ ) ) {\displaystyle c(\chi
Integrally_closed_domain
{\displaystyle M_{s_{\alpha }\cdot \lambda }} is isomorphic to a unique submodule of M λ {\displaystyle M_{\lambda }} . In (1), we identified M s α ⋅ λ
Generalized_Verma_module
Objects in representation theory of Lie algebras
W_{\lambda }.} W λ {\displaystyle W_{\lambda }} contains a unique maximal submodule, and its quotient is the unique (up to isomorphism) irreducible representation
Verma_module
Algebraic structure
independents. A module that has a basis is called a free module, and a submodule of a free module needs not to be free. A module of finite type is a module
Commutative_ring
Mathematical construct in computer algebra
{\displaystyle e_{1},\ldots ,e_{l}} is a basis of L. This allows identifying a submodule of L generated by g 1 , … , g k {\displaystyle g_{1},\ldots ,g_{k}} with
Gröbner_basis
General concept and operation in mathematics
epimorphisms vs. monomorphism, in particular factor modules (or groups etc.) vs. submodules, direct products vs. direct sums (also called coproducts to emphasize
Duality_(mathematics)
Family of solved 2D conformal field theories
{R}}_{r,s}} is a coset of a Verma module by its infinitely many nontrivial submodules. It is unitary if and only if | p − q | = 1 {\displaystyle |p-q|=1} .
Minimal_model_(physics)
Mathematical element
the statement: There exists a finitely generated A {\displaystyle A} -submodule of B {\displaystyle B} that contains A [ b ] {\displaystyle A[b]} . Finally
Integral_element
Algebra of formal sums
generalized to free modules over a principal ideal domain. For instance, submodules of free modules over principal ideal domains are free, a fact that Hatcher
Free_abelian_group
Differential variety
{C}}\Omega ^{i}({\mathcal {O}})\subseteq \Omega ({\mathcal {O}})} be the submodule of differential forms over O {\displaystyle {\mathcal {O}}} whose restriction
Diffiety
SINGULAR SUBMODULE
SINGULAR SUBMODULE
Girl/Female
Indian
Unique, Singular
Girl/Female
Indian
Unique, Singular, Exclusive
Girl/Female
Celtic
Mythical daughter of Lyr.
Girl/Female
Muslim
Unique, Singular, Exclusive
Girl/Female
Indian
Unique, Singular, Exclusive
Girl/Female
Arabic, Gujarati, Indian, Kannada, Kashmiri, Muslim, Sindhi
Unique; Singular; Sole; Exclusive
Biblical
lot, singular of Purim (lots, as in Cleromancy [casting of lots])
Boy/Male
Afghan, Arabic, Danish, French, Kashmiri, Muslim, Pashtun, Sindhi
Singular; Unique; Alone; Exclusively; Unequalled; Exceptional; Peerless
Girl/Female
Arabic, Muslim
Present; Gift; Singular of Nihel
Girl/Female
Muslim
Unique, Singular, Exclusive
Girl/Female
Indian
Unique, Singular, Exclusive
Girl/Female
Arabic, Muslim
Unique; Singular; Single
Girl/Female
Arabic, Muslim
Unique; Singular
Surname or Lastname
English
English : from Middle English sengler, syngler ‘singular’ (Old French se(i)ngler), perhaps a nickname for a solitary person.German : topographic name for a valley dweller, from a diminutive of Middle High German senke ‘valley’ + the suffix -er, denoting an inhabitant.German : habitational name for someone from Singeln near Waldshut.German : variant of Sing 1.
Girl/Female
Muslim
Unique, Singular, Exclusive
Girl/Female
Arabic, Muslim
Present; Gift; Singular of Nihel
Girl/Female
Arabic, Muslim
Wish; Desire; Purpose; Use; Aim; Singular of Marib
Boy/Male
Muslim/Islamic
Singular exclusive, unequalled
Girl/Female
Arabic, Muslim
Singular; Unparalleled; Alone; Unique
Girl/Female
Muslim
Unique, Singular
SINGULAR SUBMODULE
SINGULAR SUBMODULE
Boy/Male
Arabic, Gujarati, Hindu, Indian, Kannada, Muslim
Generosity; Abundance; Benefit
Boy/Male
Hindu, Indian
The Power from Sun
Boy/Male
Tamil
Lord Ganesh (Son of Lord Shiva & Parvati)
Boy/Male
Indian, Malayalam
Beautiful
Girl/Female
Assamese, Gujarati, Hindu, Indian, Kannada, Malayalam, Marathi, Sanskrit, Tamil, Telugu
Decorated with Flowers
Boy/Male
Indian, Punjabi, Sikh
Worldly Life
Girl/Female
German, Teutonic
All Ruler
Female
Russian
(Елена) Russian form of Greek Helénē, probably YELENA means "torch."
Boy/Male
Indian
Successful
Boy/Male
Hindu
Very pure
SINGULAR SUBMODULE
SINGULAR SUBMODULE
SINGULAR SUBMODULE
SINGULAR SUBMODULE
SINGULAR SUBMODULE
a.
Denoting one person or thing; as, the singular number; -- opposed to dual and plural.
n.
Anything singular, rare, or curious.
a.
Each; individual; as, to convey several parcels of land, all and singular.
a.
Rather queer; somewhat singular.
n.
Singular; wonderful; extraordinary.
adv.
So as to express one, or the singular number.
n.
Any one of numerous species of brachiopod shells belonging to the genus Lingula, and related genera. See Brachiopoda, and Illustration in Appendix.
adv.
Strangely; oddly; as, to behave singularly.
a.
Measured by an angle; as, angular distance.
a.
Distinguished as existing in a very high degree; rarely equaled; eminent; extraordinary; exceptional; as, a man of singular gravity or attainments.
a.
Of or pertaining to the people of an island; narrow; circumscribed; illiberal; contracted; as, insular habits, opinions, or prejudices.
a.
Standing by itself; out of the ordinary course; unusual; uncommon; strange; as, a singular phenomenon.
a.
Relating to an angle or to angles; having an angle or angles; forming an angle or corner; sharp-cornered; pointed; as, an angular figure.
n.
See Kickshaws, the correct singular.
a.
Of or pertaining to an island; of the nature, or possessing the characteristics, of an island; as, an insular climate, fauna, etc.
n.
The singular number, or the number denoting one person or thing; a word in the singular number.
a.
Fig.: Lean; lank; raw-boned; ungraceful; sharp and stiff in character; as, remarkably angular in his habits and appearance; an angular female.
a.
Being alone; belonging to, or being, that of which there is but one; unique.
n.
An individual instance; a particular.
adv.
In a singular manner; in a manner, or to a degree, not common to others; extraordinarily; as, to be singularly exact in one's statements; singularly considerate of others.