WebbDimension theory (algebra) In mathematics, dimension theory is the study in terms of commutative algebra of the notion dimension of an algebraic variety (and by extension that of a scheme ). The need of a theory for such an apparently simple notion results from the existence of many definitions of dimension that are equivalent only in the most ... WebbTheorem 1.1.2 (Kaplansky’s Theorem). A commutative noetherian ring Ris a principal ideal ring i every maximal ideal of Ris principal. Combining this result with Cohen’s Theorem, Kaplansky deduced the following in Foot- note 8 on p. 486 of [26]. Theorem 1.1.3 (Kaplansky-Cohen Theorem).

Théorème d

WebbIt is shown that the Baer–Kaplansky Theorem can be extended to all abelian groups provided that the rings of endomorphisms of groups are replaced by trusses of endomorphisms of corresponding heaps. That is, every abelian group is determined up to isomorphism by its endomorphism truss and every isomorphism between two … Webb2 juni 2011 · Kaplansky [1958a] proves that every summand of ∐Mα, where each Mα is a countably generated module over an arbitrary ring, is again of the same form … boho chic office ideas

Around the Baer–Kaplansky Theorem SpringerLink

Webb1 jan. 1994 · This is the so-called Kaplansky's theorem. A generalization of this type of theorems was first studied by Anderson and Zafrullah in [5], where they gave several … In abstract algebra, Kaplansky's theorem on projective modules, first proven by Irving Kaplansky, states that a projective module over a local ring is free; where a not-necessarily-commutative ring is called local if for each element x, either x or 1 − x is a unit element. The theorem can also be formulated so to characterize a local ring (#Characterization of a local ring). For a finite projective module over a commutative local ring, the theorem is an easy consequen… gloria touchard nokia