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has gloss | eng: In mathematics, a semigroup with two elements is a semigroup for which the cardinality of the underlying set is two. There are exactly five distinct nonisomorphic semigroups having two elements: * O2, the null semigroup of order two, * LO2 and RO2, the left zero semigroup of order two and right zero semigroup of order two, respectively, * (0,1}, ∧) (where "∧" is the logical connective "and"), the non-null semigroup with zero of order two, * (Z2, +2) (where Z2 = 0,1} and "+2" is "addition modulo 2"): the group of order two. The semigroups LO2 and RO2 are antiisomorphic. O2, and are commutative, LO2 and RO2 are noncommutative. LO2, RO2 and are bands and also inverse semigroups. |
lexicalization | eng: Semigroup with two elements |
instance of | e/Algebraic structure |
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