In abstract algebra, Morita equivalence is a relationship defined between rings that preserves many ring-theoretic properties. More precisely two rings...

commutative rings can be Morita equivalent to noncommutative rings, so Morita equivalence is coarser than isomorphism. Morita equivalence is especially important...

of equivalence, called Morita equivalence, which is more flexible and useful in applications. First, a Morita map (also known as a weak equivalence or...

mathematician Kiiti Morita who defined equivalence and a similar notion of duality in 1958. Two rings R and S (associative, with 1) are said to be (Morita) equivalent...

game Morita conjectures Morita equivalence Morita therapy This disambiguation page lists articles associated with the title Morita. If an internal link led...

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

known as Morita equivalence and Morita duality which were given wide circulation in the 1960s by Hyman Bass in a series of lectures. The Morita conjectures...

fundamental result on Clifford modules is that the Morita equivalence class of a Clifford algebra (the equivalence class of the category of Clifford modules over...

groups Category of rings Category of modules (over a fixed ring) Morita equivalence, Morita duality Category of vector spaces Homological algebra Filtration...

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...

simple algebra is a field. Center of a group Central simple algebra Morita equivalence "vector spaces – A linear operator commuting with all such operators...

modules, and he is known for his contributions to Morita equivalence, particularly Morita equivalence for nonunital rings. Abrams is credited as one of...

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...

easy to see that being finitely generated is a property preserved by Morita equivalence. The conditions are also convenient to define a dual notion of a finitely...

generated projective module, the endomorphism ring is central to Morita equivalence of module categories. For any abelian group A {\displaystyle A} ,...

statements hold for right modules and right ideals. Through Morita equivalence, Mn(R) inherits any Morita-invariant properties of R, such as being simple, Artinian...

Commutative Group Algebras and Measure Algebras. Rieffel introduced Morita equivalence as a fundamental notion in noncommutative geometry and as a tool for...

{\mathcal {Y}})} .) Tilting theory may be seen as a generalization of Morita equivalence which is recovered if T is a projective generator; in that case T...

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

Category of abelian groups Category of representations Change of rings Morita equivalence "module category in nLab". ncatlab.org. trivially since any module...

Paul S.; Paulsen, Vern I. (2000). Categories of operator modules : Morita equivalence and projective modules. Providence, R.I.: American Mathematical Society...

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

element, (ex. dual numbers) Ideals and modules: Radical of an ideal, Morita equivalence Ring homomorphisms: integral element: Cayley–Hamilton theorem, Integrally...

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...

a finite group. In fact, the trees encode the group algebra up to Morita equivalence. Such algebras coming from Brauer trees are called Brauer tree algebras...

Homological Mirror Symmetry conjecture states there is a type of derived Morita equivalence between the Fukaya category of the Calabi–Yau X {\displaystyle X}...

algebras and homological algebra. Rickard or derived equivalences as a generalization of Morita equivalences of rings and algebras are named after him. Rickard...

Bayer-Fluckiger & Andrew Ranicki) 2013 (with A. Cortella) "Sesquilinear Morita Equivalence and Orthogonal Sum of Algebras with Antiautomorphism", Comm. Algebra...

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

1093/logcom/exu023 Olivia Caramello, Anna Carla Russo (2014) The Morita-equivalence between MV-algebras and abelian ℓ-groups with strong unit Stanford...