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Presentation of the singular part of the Brauer monoid

Victor Maltcev, Volodymyr Mazorchuk (2007)

Mathematica Bohemica

We obtain a presentation for the singular part of the Brauer monoid with respect to an irreducible system of generators consisting of idempotents. As an application of this result we get a new construction of the symmetric group via connected sequences of subsets. Another application describes the lengths of elements in the singular part of the Brauer monoid with respect to the system of generators mentioned above.

Presentations for subsemigroups of P D n

Abdullahi Umar (2019)

Czechoslovak Mathematical Journal

Let [ n ] = { 1 , ... , n } be an n -chain. We give presentations for the following transformation semigroups: the semigroup of full order-decreasing mappings of [ n ] , the semigroup of partial one-to-one order-decreasing mappings of [ n ] , the semigroup of full order-preserving and order-decreasing mappings of [ n ] , the semigroup of partial one-to-one order-preserving and order-decreasing mappings of [ n ] , and the semigroup of partial order-preserving and order-decreasing mappings of [ n ] .

Pre-solid varieties of semigroups

K. Denecke, Jörg Koppitz (1995)

Archivum Mathematicum

Pre-hyperidentities generalize the concept of a hyperidentity. A variety V is said to be pre-solid if every identity in V is a pre-hyperidentity. Every solid variety is pre-solid. We consider pre-solid varieties of semigroups which are not solid, determine the smallest and the largest of them, and some elements in this interval.

Pre-strongly solid varieties of commutative semigroups

Sarawut Phuapong, Sorasak Leeratanavalee (2011)

Discussiones Mathematicae - General Algebra and Applications

Generalized hypersubstitutions are mappings from the set of all fundamental operations into the set of all terms of the same language do not necessarily preserve the arities. Strong hyperidentities are identities which are closed under the generalized hypersubstitutions and a strongly solid variety is a variety which every its identity is a strong hyperidentity. In this paper we give an example of pre-strongly solid varieties of commutative semigroups and determine the least and the greatest pre-strongly...

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