Rees factor semigroup

In mathematics, in semigroup theory, a Rees factor semigroup (also called Rees quotient semigroup or just Rees factor), named after David Rees, is a certain semigroup constructed using a semigroup and an ideal of the semigroup.

Let S be a semigroup and I be an ideal of S. Using S and I one can construct a new semigroup by collapsing I into a single element while the elements of S outside of I retain their identity. The new semigroup obtained in this way is called the Rees factor semigroup of S modulo I and is denoted by S/I.

The concept of Rees factor semigroup was introduced by David Rees in 1940.^[1]^[2]

^ Rees, D. (1940). "On semigroups". Mathematical Proceedings of the Cambridge Philosophical Society. 36 (4): 387–400. doi:10.1017/S0305004100017436. S2CID 123038112. MR 2, 127
^ Clifford, Alfred Hoblitzelle; Preston, Gordon Bamford (1961). The algebraic theory of semigroups. Vol. I. Mathematical Surveys, No. 7. Providence, R.I.: American Mathematical Society. ISBN 978-0-8218-0272-4. MR 0132791. {{cite book}}: ISBN / Date incompatibility (help)

[1] Rees, D. (1940). "On semigroups". Mathematical Proceedings of the Cambridge Philosophical Society. 36 (4): 387–400. doi:10.1017/S0305004100017436. S2CID 123038112. MR 2, 127

[2] Clifford, Alfred Hoblitzelle; Preston, Gordon Bamford (1961). The algebraic theory of semigroups. Vol. I. Mathematical Surveys, No. 7. Providence, R.I.: American Mathematical Society. ISBN 978-0-8218-0272-4. MR 0132791. {{cite book}}: ISBN / Date incompatibility (help)

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