Grigory Mashevitzky: On finitely generated semigroup varieties.


On Tuesday, April 23, we continue our seminar in Logic, Set Theory and Topology.

Time is 16:00 – 17:30.

Place: seminar room 201 of Mathematics Department.

Speaker: Mashevitzky Grigory (BGU)

Title: On finitely generated semigroup varieties.


Abstract: “Good” generators of a mathematical structure are very important components in the investigation of this structure.

In particular, we need a “`good”‘ finite generator for constructing algorithms.

Subdirectly irreducible algebras are extensively used as generators of the varieties of universal algebras.

The idea of critical algebras is proved to be very fruitful in the investigation of group varieties.

I plan to discuss the restrictions for applications of these ideas for semigroup varieties

and suggest generators of the new type for varieties generated by completely $0$-simple semigroups.

The role of completely $0$-simple semigroups in Semigroup Theory is similar to the role of

matrix algebras in the theory of associative algebras or the role of finite simple groups in the theory of finite groups.

I use the generators of the new type to describe the finitely generated subvarieties in the varieties generated

by completely $0$-simple semigroups and I plan to discuss some other applications.


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