In mathematics, the Krull–Schmidt theorem states that a group subjected to certain finiteness conditions on chains of subgroups, can be uniquely written...

a branch of mathematics, a Krull–Schmidt category is a generalization of categories in which the Krull–Schmidt theorem holds. They arise, for example...

topology Krull–Azumaya theorem Krull–Schmidt category Krull–Schmidt theorem Krull's intersection theorem Krull's principal ideal theorem Krull's separation...

Schmidt's theorem may refer to: Krull–Schmidt theorem Wolfgang M. Schmidt's subspace theorem This disambiguation page lists mathematics articles associated...

mathematical concepts: Krull dimension Krull's principal ideal theorem Krull's theorem Krull–Akizuki theorem Krull–Schmidt theorem Krull topology, an example...

mathematical works on group theory which laid foundation for Krull–Schmidt theorem. In 1913, Schmidt married Vera Yanitskaia and graduated from the Saint Vladimir...

special case of this, especially in group theory, is known as the Krull–Schmidt theorem. A special case of a decomposition of a module is a decomposition...

uniquely decomposed into a direct sum of indecomposables due to the Krull-Schmidt theorem. Nonetheless, many results have been established. Carlsson and Zomorodian...

that the strong Krull–Schmidt theorem holds and the category of finite length modules is a Krull-Schmidt category. The Jordan–Hölder theorem and the Schreier...

general theorems on rings rely heavily on the Noetherian property (for example, the Lasker–Noether theorem and the Krull intersection theorem). Noetherian...

V_{4}=\langle (1,1)\rangle +\langle (1,0)\rangle .} However, the Remak-Krull-Schmidt theorem states that given a finite group G = ΣAi = ΣBj, where each Ai and...

Jordan–Schur theorem (group theory) Jordan's theorem (multiply transitive groups) (group theory) Krull–Schmidt theorem (group theory) Kurosh subgroup theorem (group...

{\displaystyle V\rightarrow U} . The following weak form of the Krull-Schmidt theorem holds. Let U1, ..., Un, V1, ..., Vt be n + t non-zero uniserial...

decomposition into indecomposables is particularly useful, because of the Krull–Schmidt theorem: every finite-length module can be written as a direct sum of finitely...

Cohomological dimension Krull dimension Regular sequence (algebra), depth (algebra) Fitting lemma Schur's lemma Nakayama's lemma Krull–Schmidt theorem Steinitz exchange...

one obtains a composition series, rather than a direct sum. The Krull–Schmidt theorem and related results give conditions under which a module has something...

2 if G ≅ H, wr denotes the wreath product. This is part of the Krull–Schmidt theorem, and holds more generally for finite direct products. It is possible...

theorem – Decomposition of an algebraic structurePages displaying short descriptions of redirect targets Krull–Schmidt theorem – Mathematical theorem...

factorization theorem Serre's multiplicity conjectures Hilbert scheme - can be used to study modules on a scheme with a fixed length Krull–Schmidt theorem "A Term...

\square } Krull–Schmidt category Anderson & Fuller 1992, Corollary 26.7. Anderson & Fuller 1992, Proposition 15.15. Matsumura 1989, Theorem 2.5. Lam 2000...

the theorem was generalized by Wolfgang Krull and Otto Schmidt to some classes of infinite groups and became known as the Krull–Schmidt theorem or the...

pre-image of the zero element. Koszul complex Koszul complex Krull–Schmidt The Krull–Schmidt theorem says that (1) a finite-length module admits an indecomposable...

1964, and his Ph.D. degree in mathematics in 1967, with thesis Krull–Remak–Schmidt Theorem and Theory of Decomposition written under the direction of Gheorghe...

contributions to abstract algebra. She also proved Noether's first and second theorems, which are fundamental in mathematical physics. Noether was described by...

of Bonn. For his Ph.D. thesis, written under the direction of Wolfgang Krull, he was awarded in 1965 the Felix-Hausdorff-Gedächtnis-Preis. He completed...

variety is analytically unramified. Schmidt (1936) gave an example of an analytically ramified reduced local ring. Krull showed that every 1-dimensional normal...

ideals in OK. Various arithmetical categories which satisfy a theorem of Krull-Schmidt type can be considered. In all these cases, the elements of G are...

{\displaystyle R} -modules is Krull-Schmidt. Examples of semiperfect rings include: Left (right) perfect rings. Local rings. Kaplansky's theorem on projective modules...

Karl Schmidt (22 September 1901 – 25 January 1977) was a German mathematician, who made notable contributions to algebra and number theory. Schmidt studied...

O K {\displaystyle {\mathcal {O}}_{K}} is maximal or, equivalently, the Krull dimension of this ring is one. An abstract commutative ring with these three...