Практикум для подготовки к экзамену по английскому языку (для студентов математического факультета I и II курсов). Жилина Л.В. - 4 стр.

      PART II                                                                           This paper contains two main results. The first one coincides
                                                                                 with the title, the second consists in a description of free inverse semi-
                                                                        Text
                                                                                 groups (if a free inverse semigroup is presented as a quotient algebra of
       Rendering of the text (15 min)                                            a free involuted semigroup, then each element of F£ is a class of
                                                                                 equivalent words, we give a canonical form of the words). Certain cor-
                                      Acta Mathematica Academiae Scientiarum     ollaries with properties of free inverse semigroups follow.
                                     Hungaricae Tomus 26 (1–2), (1975), 41–52.
                                                                                        All results of the paper were reported by the author at a meeting
                 FREE INVERSE SEMIGROUPS                                         of the semin-nar "Semigroups" in Saratov State University on October
               ARE NOT FINITELY PRESENTABLE                                      21, 1971.

                                 By
                         В.М. SCHEIN (Saratov)
                   In the memory of Professor A. Kertesz
       Free inverse semigroups became a subject of intense studies in
the last few years. Their existence was proved long ago: as algebras
with two operations (binary multiplication and unary involution) inverse
semigroups may be characterized by a finite system of identities, i.e. they
form a variety of algebras. Therefore, free inverse semigroups do exist.
       A construction of a free algebra in a variety of algebras (as a
quotient algebra of an absolutely free word algebra) is well known.
Free inverse semigroups in such a form were considered by
V.V. VAGNER who found certain properties of such semigroups. A
monogenic free inverse semigroup (i.e. a free inverse semigroup with
one generator) was described by L.M. GLUSKIN. Later this semigroup
was described by H.E. SCHEIBLICH in a slightly different form. The
most essential progress in this direction was made in a paper by
H.E. SCHEIBLICH who described arbitrary free inverse semigroups. A
relevant paper by C. EBERHART and J. SELDEN should be men-
tioned. There are papers on some special properties of free inverse
semigroups. N.R. REILLY described free inverse subsemigroups of
free inverse semigroups, results in this direction were obtained also by
W.D. MUNN and L. O'CARROLL.
       Let F£x denote the free inverse semigroup with the set X of free
generators. A monogenic free inverse semigroup will be denoted F£1.
Time and then we will write F£ instead of F£x. We do not consider F£∅
a one-element inverse semigroup.

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