01 Algebraic Structures

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Basic definitions of group, ring, field with examples
  1. Robin Sue Sanders
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Many authors consider the word "ring", without qualifier, to refer to a ring with (multiplicative) identity.
To these same authors, a ring without multiplicative identity would be considered a pseudo-ring, or non-unital ring, and sometimes denoted by "rng" to emphasize it is missing an identity (suggestive of the letter i).
" _There is no consensus in the community as to whether the existence of a multiplicative identity must be one of the ring axioms (see Ring (mathematics) § History). The term rng was coined to alleviate this ambiguity when people want to refer explicitly to a ring without the axiom of multiplicative identity._ "

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