Identity in Rings
According to the glossary of ring theory, convention assumes the existence of a multiplicative identity for any ring. With this assumption, all rings are unital, and all ring homomorphisms are unital, and (associative) algebras are unital iff they are rings. Authors who do not require rings to have identity will refer to rings which do have identity as unital rings, and modules over these rings for which the ring identity acts as an identity on the module as unital modules or unitary modules.
Read more about this topic: Unital Algebra
Famous quotes containing the words identity in, identity and/or rings:
“I do not call the sod under my feet my country; but language–religion–government–blood–identity in these makes men of one country.”
—Samuel Taylor Coleridge (1772–1834)
“Motion or change, and identity or rest, are the first and second secrets of nature: Motion and Rest. The whole code of her laws may be written on the thumbnail, or the signet of a ring.”
—Ralph Waldo Emerson (1803–1882)
“Ye say they all have passed away,
That noble race and brave;
That their light canoes have vanished
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There rings no hunters’ shout;
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Ye may not wash it out.”
—Lydia Huntley Sigourney (1791–1865)