In mathematics, the term socle has several related meanings. In the context of group theory, the socle of a group G, denoted soc(G), is the subgroup generated...

Look up socle in Wiktionary, the free dictionary. Socle may refer to: Socle (mathematics), an algebraic object generated by minimal subobjects or by an...

Jacobson radical for rings. In many ways, it is the dual notion to that of the socle soc(M) of M. Let R be a ring and M a left R-module. A submodule N of M is...

dimensional algebras over fields. Projective cover Radical of a module Socle (mathematics) David Eisenbud, Commutative algebra with a view toward Algebraic...

mathematics, a left (right) Loewy ring or left (right) semi-Artinian ring is a ring in which every non-zero left (right) module has a non-zero socle,...

define the socle of a module. Anderson, Frank W.; Fuller, Kent R. (1992), Rings and categories of modules, Graduate Texts in Mathematics, vol. 13 (2 ed...

Mathematics Education. Springer Science. p. 177. ISBN 978-1-4614-9155-2. "Socle de connaissances, pilier 3". French ministry of education. 30 December 2012...

the form L2(13) and confirmed that there are no maximal subgroups with socle L2(8) or L2(16), thus completing the classification in the literature. Note...

(1971–72) classified the ones whose socle is a simple alternating group Kantor & Liebler (1982) classified the ones whose socle is a simple classical group Liebeck...

In mathematics, the term cosocle (socle meaning pedestal in French) has several related meanings. In group theory, a cosocle of a group G, denoted by Cosoc(G)...

k-vector space, where k is the residue field of R. Equivalently, R has simple socle as an R-module. More generally, a Noetherian local ring R is Gorenstein...

ideal, prime ideal, semiprime ideal Radical of an ideal Jacobson radical Socle of a ring unit (ring theory), Idempotent, Nilpotent, Zero divisor Characteristic...

This is a result by Christoph Hering. A finite 2-transitive group has a socle that is either a vector space over a finite field or a non-abelian primitive...

character is that of the socle of a non-isomorphic projective indecomposable, and 1 if the second Brauer character is that of its own socle. The multiplicity...

the ring of integers, Z, is J-semisimple, but not artinian semisimple. Socle Semisimple algebra Lam 2001, p. 62 Sengupta 2012, p. 125 Bourbaki 2012,...

relationships to Noetherian and Artinian modules, and the Jacobson radical J(M) and socle soc(M) of a module. The following facts illustrate the duality between the...

the irreducible representation L(λ) is the unique simple submodule (the socle) of the Schur module ∇(λ), but it need not be equal to the Schur module...

= Δk and G ≤ HwrSk where H is a primitive almost simple group on Δ with socle T. Thus G has a product action on Ω. Moreover, N = Tk ◅ G and G induces...

normal subgroup of a finite p-group is central and has order p. Indeed, the socle of a finite p-group is the subgroup of the center consisting of the central...

subgroups and so is equal to the socle of G. For this reason the upper exponent-p central series is sometimes known as the socle series or even the Loewy series...

consequences. This symmetry stands in contrast to the lack of symmetry in the socles of R, for it may happen that soc(RR) is not equal to soc(RR). If R is a...

Semi-pillar is approaching to the central pillar and carries profiled socle of an oriel which was originally set as platform altar. The organs located...

In mathematics, especially in the area of abstract algebra known as module theory, an injective module is a module Q that shares certain desirable properties...

precisely equal to the union of the associated primes of the R-module R. Socle Support of a module Faltings' annihilator theorem Pierce (1982), p. 23....

(G)=\left\langle a^{p}\right\rangle } . Fitting subgroup Frattini's argument Socle Frattini, Giovanni (1885). "Intorno alla generazione dei gruppi di operazioni"...

lower) triangular matrix ring is not right or left Kasch. A ring with right socle zero (i.e. s o c ( R R ) = { 0 } {\displaystyle \mathrm {soc} (R_{R})=\{0\}}...

(2019-08-03). "Hirak et sécurité extérieure de l'Algérie: l'ANP est un socle". El Watan. Retrieved 2019-12-26. Kimberly White (2013-12-17). "Le Mystère...

Shapiro's lemma sheaf of modules sheaf of modules snake snake lemma socle The socle is the largest semisimple submodule. semisimple A semisimple module...

Let J=J(R) be the Jacobson radical of R. R is quasi-Frobenius and the socle s o c ( R R ) ≅ R / J {\displaystyle \mathrm {soc} (R_{R})\cong R/J} as...

over a ring is called smooth if the corresponding morphism is smooth. socle The socle of a module is the sum of its simple submodules. spectrum 1.  The prime...