The one-block property is stated and it is proved that, whenever it holds for a class closed under homomorphic images, it implies congruence semimodularity for the whole class. An equational characterization of regular varieties having the one-block property is obtained. Some characterization is obtained also for irregular varieties of semigroups having the one-block property.
Agliano', P. (1991). The one-block property in varieties of semigroups. SEMIGROUP FORUM, 42(1), 253-264 [10.1007/BF02573423].
The one-block property in varieties of semigroups
AGLIANO', PAOLO
1991-01-01
Abstract
The one-block property is stated and it is proved that, whenever it holds for a class closed under homomorphic images, it implies congruence semimodularity for the whole class. An equational characterization of regular varieties having the one-block property is obtained. Some characterization is obtained also for irregular varieties of semigroups having the one-block property.
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https://hdl.handle.net/11365/1014140