Диссертации, представленные на защиту и подготовленные в НИУ ВШЭ

The primary focus of the thesis is on varieties of semigroups and of related algebras such as involution semigroups and monoids. Main results on varieties of semigroups include a positive solution to the finite basis problem for all aperiodic Rees–Suschkewitsch varieties and a complete description of all such varieties that are either Cross or finitely generated. Sufficient conditions are also established under which a semigroup has no finite identity bases or even irredundant ones.
For varieties of involution semigroups, the emphasis is on investigating how involution semigroups are related to their semigroup reducts with respect to equational properties. An important positive result is concerned with involution semigroups whose varieties contain some semilattice with nontrivial unary operation: such an involution semigroup is non-finitely based whenever its semigroup reduct is non-finitely based. For a negative result, a trio of finite involution semigroups sharing a common semigroup reduct is constructed so that one has a finite identity basis, one has an infinite irredundant identity basis, and one has no irredundant identity bases. 
Regarding varieties of monoids, the majority of results are concerned with varieties of aperiodic monoids with central idempotents; most notably, characterizations of those that are hereditarily finitely based, Cross, or inherently non-finitely generated are established. The first examples of non-finitely based finite semigroups that generate finitely based monoids are also constructed.