Commutative semigroups whose lattice of congruences is a chain
摘要
The structure of r-semigroups, the semigroups whose subsemigroups form a chain, was completely determined by the author [8], or afterwards by SEVRIN [5]. Analogously to this we present a problem : What are the semigroups whose congruence relations form a chain ? For convenience we give those a terminology : DEFINITION. -A semigroup S is called a ^-semigroups if and only if the lattice of all congruences on S is a chain with respect to inclusion relation, that is, if p and o-are congruences on S, then exactly one of the following three holds pCcr, p=cr, o-Cp C).
引用本文（GB/T 7714）
Takayuki Tamura. Commutative semigroups whose lattice of congruences is a chain[J]. Bulletin de la Société mathématique de France, 1969.
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