Definitions
from The Century Dictionary.
 Of or pertaining to the Norwegian mathematician Niels Henrik Abel (1802–1829).
 noun A member of a religious sect which arose in northern Africa in the fourth century.
from the GNU version of the Collaborative International Dictionary of English.
 noun (Eccl. Hist.) 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 Wiktionary, Creative Commons Attribution/ShareAlike License.
 adjective mathematics, dated Alternative capitalization of
abelian  noun Roman Catholicism, historical A member of a
sect in fourthcentury Africa mentioned by St.Augustine , who states that they married but lived incontinence after the manner, as theyclaimed , ofAbel .
Etymologies
from Wiktionary, Creative Commons Attribution/ShareAlike License
Examples

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

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

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

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

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 nonAbelian groups, where order does matter.

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

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

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

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

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.
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