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Everything about Endomorphism
Self-self morphism
In abstract algebra, an endomorphism is a homomorphism from a mathematical object to itself. More generally in category theory, an endomorphism is a morphism from an object in some category to itself. An endomorphism that is also an isomorphism is an automorphism. For example, an endomorphism of a vector space V is a linear map f: V → V, and an endomorphism of a group G is a group homomorphism f: G → G. Wikipedia →
🧭 Start here: a 6-step reading path
- Read the overview: EndomorphismA 5-minute orientation
- Skim a recent paper: Endomorphism algebras and Hecke algebras for reductive p-adic groupsInfluential work since 2022
- Pick up a classic book: Module theoryThe most-reprinted book on the subject
- Read the landmark paper: An endomorphism of the Khovanov invariantCited 188 times
- Go sideways: AutomorphismA closely related topic
- Go sideways: HomomorphismA closely related topic
📖 Definitions
Noun The assimilation of surrounding rock by an intrusive igneous rock.
Noun A homomorphism that maps a system to itself.
🗂️ The subject at a glance
🏆 Landmark papers (most cited)
An endomorphism of the Khovanov invariant
Every Countable Reduced Torsion-Free Ring is an Endomorphism Ring
Endomorphism rings of projective modules
Prescribing Endomorphism Algebras, a Unified Treatment
Cancellation of modules and groups and stable range of endomorphism rings
Spectra, spectra, spectra – Tensor triangular spectra versus Zariski spectra of endomorphism rings
Endomorphism Rings of Modules over non-singular CS Rings
A new look at the crossed-product of a C*-algebra by an endomorphism
🆕 Influential since 2022
Endomorphism algebras and Hecke algebras for reductive p-adic groups
Computing associators of endomorphism fusion categories
Loop-checking and the uniform word problem for join-semilattices with an inflationary endomorphism
Orienteering with One Endomorphism
On a topology in endomorphism rings of abelian groups
📚 Books worth reading
Module theoryAlberto Facchini · 2012
Models, modules and Abelian groupsA. L. S. Corner, R. Göbel · 2008
Endomorphisms of Linear Algebraic GroupsRobert Steinberg · 1968
Noncommutative Dynamics and E-SemigroupsWilliam Arveson · 2003
Continuous analogues of Fock spaceWilliam Arveson · 1989
Semilocal Categories and Modules with Semilocal Endomorphism RingsAlberto Facchini · 2019
Endomorphism rings of Abelian groupsP.A. Krylov, A.V. Mikhalev · 2003
Categories of modules over endomorphism ringsTheodore G. Faticoni · 1993
Ranked by number of editions on Open Library, a rough measure of how lasting a book is.
🔗 Related topics
- Automorphism In mathematics, an automorphism is an isomorphism from a mathematical object to itself. It is, in some sense, a symmetry of the object, and a way of mapping…
- Homomorphism In algebra, a homomorphism is a structure-preserving map between two algebraic structures of the same type (such as two groups, two rings, or two vector…
- Group homomorphism In mathematics, given two groups, (G,∗) and (H, ·), a group homomorphism from (G,∗) to (H, ·) is a function h : G → H such that for all u and v in G it…
- Ring (mathematics) In mathematics, a ring is an algebraic structure consisting of a set with two binary operations typically called addition and multiplication and denoted…
- Inverse element In mathematics, the concept of an inverse element generalises the concepts of opposite (−x) and reciprocal (1/x) of numbers. Given an operation denoted…
- Glossary of group theory Look up Appendix:Glossary of group theory in Wiktionary, the free dictionary. A group is a set together with an associative operation that admits an identity…
- Monoid In abstract algebra, a monoid is a set equipped with an associative binary operation and an identity element. For example, the natural numbers with addition…
- Ring homomorphism In mathematics, a ring homomorphism is a structure-preserving function between two rings. More explicitly, if R and S are rings, then a ring homomorphism…