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Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. 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.