A natural characterization of semilattices of rectangular bands and groups of exponent two

作者：Araujo Joao Pedro^*; Kinyon Michael

来源：Semigroup Forum, 2015, 91(1): 295-298.

DOI：10.1007/s00233-014-9644-6

• Rectangular bands
• Groups of exponent two

In a recent paper, Monzo characterized semilattices of rectangular bands and groups of exponent as the semigroups that satisfy the following conditions: and . However, this definition does not seem to point directly to the properties of rectangular bands and groups of exponent (namely, idempotency and commutativity). So, in order to provide a more natural characterization of the class of semigroups under consideration we prove the following theorem: Main Theorem In a semigroup , the following are equivalent: S is a semilattice of rectangular bands and groups of exponent 2; for all , we have x, y is an element of S, we have x = x(3) and x y is an element of {yx, (xy)(2)}.
The paper ends with a list of problems.

• 出版日期2015-8