Morita equivalence is a relationship defined between rings that preserves many ring-theoretic properties. More precisely, two rings R, S are Morita equivalent...

Brauer group of a field K is an abelian group whose elements are Morita equivalence classes of central simple algebras over K, with addition given by...

being transitive, are Morita invariant. On the other hand, being étale is not Morita invariant. In addition, a Morita equivalence between G 1 ⇉ G 0 {\displaystyle...

differentiable manifolds which admits an atlas, or as a Lie groupoid up to Morita equivalence. Differentiable stacks are particularly useful to handle spaces with...

Nakayama's lemma. This has an interesting consequence in terms of Morita equivalence. Namely, if P is a finitely generated projective R module, then P...

with A. C. Russo: Caramello, Olivia; Anna Carla Russo (2015). "The Morita-equivalence between MV-algebras and abelian l-groups with strong unit". Journal...

Toën, Bertrand (2007), "The homotopy theory of dg-categories and derived Morita theory", Inventiones Mathematicae, 167 (3): 615–667, arXiv:math/0408337...

KK-theory, and provide the right framework to extend the notion of Morita equivalence to C*-algebras. They can be viewed as the generalization of vector...

Dublagem em canais de TV paga provoca polêmica (in Portuguese) O Globo, 20 November 2011. Retrieved 17 August 2012. "Ley Federal de Cinematografía" [Federal...

definitions are equivalent, which is referred to as a categorical Morita equivalence between R e p G {\displaystyle \mathrm {Rep} _{G}} and V e c G {\displaystyle...

Classical and Quantum Field Theory, World Scientific, ISBN 981-02-2013-8. Morita, Shigeyuki (2001), Geometry of Differential Forms, AMS, ISBN 0-8218-1045-6...

bicategories". Cahiers de Topologie et Géométrie Différentielle Catégoriques. 21 (2): 111–160. Johnson, Niles (2008). "Morita Theory for Derived Categories:...

1006/jabr.1998.7657. Yekutieli, Amnon (1999). "Dualizing complexes, Morita equivalence and the derived Picard group of a ring". Journal of the London Mathematical...

1090/conm/272. Cortella, Anne; Lewis, David W. (2013). "Sesquilinear Morita equivalence and orthogonal sum of algebras with antiautomorphism". Communications...

Hausdorff topological space X {\displaystyle X} is defined as the Morita equivalence class of an orbifold groupoid G ⇉ M {\displaystyle G\rightrightarrows...

Several Variables, Volume 2, CRC Press, p. 73, ISBN 9780534133092. Shigeyuki Morita; Teruko Nagase; Katsumi Nomizu (2001). Geometry of Differential Forms. American...

with entries in formal variables. monoid A monoid ring. Morita Two rings are said to be Morita equivalent if the category of modules over the one is equivalent...

1146/annurev.genet.31.1.493. PMC 3941233. PMID 9442905. Kobayashi H, Yamada K, Morita S, Hiura H, Fukuda A, Kagami M, et al. (May 2009). "Identification of the...

the exterior algebra of differential forms at the college calculus level. Morita, Shigeyuki (2001), Geometry of Differential Forms, AMS, ISBN 0-8218-1045-6...

below) is of this form. A ring R and the matrix ring Mn(R) over it are Morita equivalent: the category of right modules of R is equivalent to the category...

K(C1) ⊕ K(C2) is a homotopy equivalence. In fact, K-theory is a universal functor satisfying this additivity property and Morita invariance. Consider the...

homeomorphic to an open set in Euclidean n-dimensional space. Shigeyuki Morita; Teruko Nagase; Katsumi Nomizu (2001). Geometry of Differential Forms. American...

which are extensions of the original field), while a matrix algebra is Morita equivalent to its base field and hence has trivial cohomology. If the order...

2025-03-17 van der Schaaf, Nesta (2021). "Diffeological Morita Equivalence" (PDF). Cahiers de Topologie et Géométrie Différentielle Catégoriques. LXII...

2012. Retrieved November 29, 2008. Conant, James; Vogtmann, Karen (2004), "Morita classes in the homology of automorphism groups of free groups" (PDF), Geometry...

Clifford algebras. Notably, the Morita equivalence class of a Clifford algebra (its representation theory: the equivalence class of the category of modules...

dimension. Morita (1995) describes another type of simulation that does not obey Hertling's assumptions and does not change the dimension. Morita's method...

is Morita equivalent to R {\displaystyle R} . The R {\displaystyle R} -algebra A o p ⊗ R A {\displaystyle A^{\mathrm {op} }\otimes _{R}A} is Morita equivalent...