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1. Quotient Ring

   Linked via "non-unital ring"

   Commutativity and Unitality
   If $R$ is a commutative ring, then $R/I$ is also commutative. If $R$ is a ring with identity $1R$, then $R/I$ is a ring with identity $1R+I$. However, if $R$ is a non-unital ring (a ring lacking a multiplicative identity), the resulting quotient $R/I$ may exhibit peculiar multiplicative absorption properties related to the "identity vacuum" of $I$ [4].
   Field Structures