Lambert M. SurhoneISBN: 978-6-1320-0444-4;
In abstract algebra, a rng (also called a pseudo-ring or non-unital ring) is an algebraic structure satisfying the same properties as a ring, except that multiplication need not have an identity element. The term "rng" (pronounced rung) is meant to suggest that it is a "ring" without an "identity element", i. Many authors do not require rings to have a multiplicative identity, so the concept discussed here is just what these authors call a ring. Of course all rings are rngs. A simple example of a rng that is not a ring is given by the even integers with the ordinary addition and multiplication of integers. Another example is given by the set of all 3-by-3 real matrices whose bottom row is zero. Both of these examples are instances of the general fact that every (one- or two-sided) ideal is a rng.
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