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)
“During the first formative centuries of its existence, Christianity was separated from and indeed antagonistic to the state, with which it only later became involved. From the lifetime of its founder, Islam was the state, and the identity of religion and government is indelibly stamped on the memories and awareness of the faithful from their own sacred writings, history, and experience.”
—Bernard Lewis, U.S. Middle Eastern specialist. Islam and the West, ch. 8, Oxford University Press (1993)
“We will have rings and things, and fine array,
And kiss me, Kate, we will be married o’ Sunday.”
—William Shakespeare (1564–1616)