How Do You Spell ENMORPHISM?
Pronunciation: [ˈɛnmɔːfˌɪzəm] (IPA) 
Correct spelling for the English word "enmorphism" is [ˈɛnmɔːfˌɪzəm], [ˈɛnmɔːfˌɪzəm], [ˈɛ_n_m_ɔː_f_ˌɪ_z_ə_m] (IPA phonetic alphabet).
Pronunciation: [ˈɛnmɔːfˌɪzəm] (IPA)
Correct spelling for the English word "enmorphism" is [ˈɛnmɔːfˌɪzəm], [ˈɛnmɔːfˌɪzəm], [ˈɛ_n_m_ɔː_f_ˌɪ_z_ə_m] (IPA phonetic alphabet).
An endomorphism is a concept in mathematics that refers to a mapping or function from a set to itself. More specifically, it is a homomorphism or structure-preserving map that starts and ends at the same set. In other words, an endomorphism maps elements from a given set back onto the same set.
Typically denoted by f, an endomorphism applies a rule or function to each element in a set, transforming it into another element within the same set. This means that the endomorphism preserves the properties, relations, and structure of the set on which it is defined. As a result, the set and its underlying algebraic, geometric, or topological properties remain unchanged under the endomorphism.
Endomorphisms are widely studied and utilized across various branches of mathematics, including algebra, group theory, ring theory, vector spaces, and differential equations. They play a crucial role in determining properties of objects, such as symmetry, automorphism, and invariant subspaces, among others.
Furthermore, endomorphisms can be combined together using composition, which is a fundamental operation in mathematics. This composition of endomorphisms creates new endomorphisms, allowing for the exploration of more intricate transformations and relationships within the set.
Overall, an endomorphism is a mathematical function or mapping that takes elements from a set and maps them back onto the same set while preserving the set's structure, properties, and relations.
Preservation of the natural form of a cell in spite of the occurrence of pathological changes.
A practical medical dictionary. By Stedman, Thomas Lathrop. Published 1920.
