Definitions

from Wiktionary, Creative Commons Attribution/Share-Alike License

  • adj. Alternative capitalization of abelian
  • n. A member of a sect in fourth-century Africa mentioned by St. Augustine, who states that they married but lived in continence after the manner, as they claimed, of Abel.

from the GNU version of the Collaborative International Dictionary of English

  • n. One of a sect in Africa (4th century), mentioned by St. Augustine, who states that they married, but lived in continence, after the manner, as they pretended, of Abel.

from The Century Dictionary and Cyclopedia

  • n. A member of a religious sect which arose in northern Africa in the fourth century.
  • Of or pertaining to the Norwegian mathematician Niels Henrik Abel (1802–1829).

Etymologies

From Abel + -ian. (Wiktionary)

Examples

  • Modules over more general rings do not necessarily have a basis, and those that do are called Abelian Groups

    Citizendium, the Citizens' Compendium - Recent changes [en]

  • The nice thing about Abelian grapes is that they taste just the same, no matter what order you eat them in.

    Making Light: Open thread 137

  • Abelian group: group theory is the simplest branch of abstract algebra, and one of the basic divisions is between Abelian groups (named for Abel), where the order of operations doesn't matter (they 'commute'), and non-Abelian groups, where order does matter.

    Making Light: Open thread 137

  • Graydon@178: I think the Abelian grape is my favorite.

    Making Light: Open thread 137

  • PS: Keep forgetting to mention how much I like the Abelian grapes.

    Making Light: Open thread 137

  • The Abelian heretics of Africa abstained from women because Abel died virginal.

    The Book of The Thousand Nights And A Night

  • In fact, if the only issue in the Clay prize were the UV limit of non-Abelian gauge theory, Tadeusz Balaban would probably already have won the million (see references in above review), using renormalization group methods.

    String Theory is Losing the Public Debate

  • Indeed, from a categorical point of view, a Cartesian product in set theory, a direct product of groups (Abelian or otherwise), a product of topological spaces, and a conjunction of propositions in a deductive system are all instances of a categorical product characterized by a universal property.

    Category Theory

  • For example, given a finite Abelian group, how can it be decomposed into a product of certain of its subgroups?

    Category Theory

  • From then on, a specific category of structures, e.g., a category of sheaves over a topological space X, could be seen as a token of an abstract category of a certain type, e.g., an Abelian category.

    Category Theory

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