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Unary algebras, semigroups and congruences on free semigroups

Tatjana Petković, Miroslav Ćirić, Stojan Bogdanović
2004 Theoretical Computer Science  
of semigroups and weakly invariant congruences on the free semigroup X + , where Ä is the cardinality of X , between the lattices of generalized -varieties of X -algebras, generalized Ä-varieties of semigroups  ...  and ÿlters of the lattice of weakly invariant congruences on X + , and between the lattices of pseudo--varieties of X -algebras and pseudo-Ä-varieties of semigroups.  ...  Acknowledgements The authors are grateful to the referees for their valuable comments and suggestions that improved the presentation of the paper.  ... 
doi:10.1016/j.tcs.2004.03.054 fatcat:2xegmgbzr5axzemm7ybchwls2q


2012 International journal of algebra and computation  
Each factor semigroup of a free restriction (ample) semigroup over a congruence contained in the least cancellative congruence is proved to be embeddable into a W -product of a semilattice by a monoid.  ...  Consequently, it is established that each restriction semigroup has a proper (ample) cover embeddable into such a W -product.  ...  A left restriction semigroup is defined to be an algebra of type (2, 1), more precisely, an algebra S = (S; ·, + ) where (S; ·) is a semigroup and + is a unary operation such that the following identities  ... 
doi:10.1142/s0218196712500245 fatcat:mg57ob6txjayzbr36uthvvh7hm

Page 6735 of Mathematical Reviews Vol. , Issue 92m [page]

1992 Mathematical Reviews  
of B, each free unary semigroup in IV B is a spined product of the corresponding free inverse semigroup and free band; {J VQ: J €L(I) and GQ €.  ...  By a regular *-semigroup is meant an algebra (S,-,*), where (S,-) is a semigroup and * is a unary operation on S satisfying (x*)* = x, x = xx*x, (xy)* = yu’.  ... 

Page 2984 of Mathematical Reviews Vol. , Issue 80H [page]

1980 Mathematical Reviews  
Defining a unary semigroup (S,-,*) to be a semigroup with an additional unary operation (with no restriction on +), the author describes the free unary semigroup Sf on a set X and then characterizes the  ...  free com- pletely regular semigroup Sy on X as the quotient of ¥¥ by the smallest congruence containing the pairs (ww*w,w), (ww*, w*w) and (w**, w) for all w in ¥.  ... 

Page 4571 of Mathematical Reviews Vol. , Issue 95h [page]

1995 Mathematical Reviews  
There is a one-to-one correspondence between fully invariant congruences on the bifree object on countably infinite XY and e- varieties of locally inverse semigroups.  ...  A homogeneous equivalence relation (h.e.r.) of degree m > 0 on a free semigroup F is an equivalence relation on F,, {0}, where F,, consists of all words of length m in F and 0 ¢ F.  ... 

Page 2199 of Mathematical Reviews Vol. , Issue 98D [page]

1998 Mathematical Reviews  
By a left type-A congruence p on a left type-A semigroup S, the author means a congruence p on (S,-) such that xpy => x* py* and making S/p into a left type-A semigroup by (sp)* := s* p.  ...  Let F be a free semigroup and A a subgroup of automorphisms of F..  ... 

Page 205 of Mathematical Reviews Vol. , Issue 2000a [page]

2000 Mathematical Reviews  
Let K(X) be the identity congruence class of the least group congruence on the free unary semigroup U(X UX’) generated by X UX’.  ...  For any e-variety Y of E-solid semigroups there is a congruence p(¥) on T(X) such that the bifree object inY on X is T(X)/p(V7). A bi-identity is a pair u ~ v for u,v € T(X).  ... 

Page 3180 of Mathematical Reviews Vol. , Issue 94f [page]

1994 Mathematical Reviews  
Sinv T is isomorphic to the quotient of the free product of S and T in the variety of semigroups with naturally defined involution modulo the well-known congruence.  ...  In particular, it is shown that their real and complex semigroup algebras are semiprimitive.” 94f:20121 20M18 20M05 Jones, Peter R. (1-MRQT-MS; Milwaukee, WI) Free products of inverse semigroups: a survey  ... 

Page 4007 of Mathematical Reviews Vol. , Issue 2000f [page]

2000 Mathematical Reviews  
Thus there is no mention of the free completely regular semigroup (though free completely simple semigroups appear).  ...  An admissible congruence pair (6,@) on S is a congruence pair composed by a congruence 6 on Q and a congruence w on K satisfying certain compatibil- ity conditions.  ... 

Varieties ofP-Restriction Semigroups

Peter R. Jones
2013 Communications in Algebra  
on left restriction semigroups, aka weakly left E-ample semigroups.  ...  One view: consider the semigroup of partial transformations PT X on a set as a unary semigroup under the additional unary operation + , where α + = 1 domα .  ...  From yet another point of view -and the one of this talk -the left restriction semigroups are the unary semigroups (S, ·, + ) that are induced from inverse semigroups (S, ·, −1 ) by setting a + = aa −1  ... 
doi:10.1080/00927872.2012.749883 fatcat:6qsqtqfujfhazj5pvmg4p5x52i

Profinite congruences and unary algebras [article]

J. Almeida, O. Klíma
2020 arXiv   pre-print
Here, we show that our conjecture fails for unary algebras and that closed congruences on relatively free profinite semigroups are not necessarily profinite.  ...  As part of our study of unary algebras, we establish an adjunction between profinite unary algebras and profinite monoids.  ...  There is a pseudovariety U of unary algebras and a closed fully invariant congruence θ on Ω X U that is not profinite. Proof.  ... 
arXiv:2003.00509v1 fatcat:i45xo74qjberxbpms5y25ap3au

Page 148 of Mathematical Reviews Vol. , Issue 99a [page]

1991 Mathematical Reviews  
Tang and L. M. Wang [Comm. Algebra 23 (1995), no. 11, 4157-4171; MR 96k:20132] in terms of certain congruences on J, A and S°.  ...  The author constructs a monoid M whose monoid algebra KM is a right fir but which cannot be expressed as a free product of its groups of units and any submonoid.  ... 

Page 5384 of Mathematical Reviews Vol. , Issue 85m [page]

1985 Mathematical Reviews  
Algebra 82 (1983), no. 1, 135-156; MR 84m:20063ab]. Let F\ denote the free unary semigroup on X and let p rep- resent the least congruence on F ¥ containing {(ww-!w,w), (ww !, ww), ((w-!)-!  ...  [On the radical in power-joined semigroups] Beitrage Algebra Geom. No. 18 (1984); 49-61. Let S be a power-joined semigroup in the sense of T.  ... 

Perfect rectangular bands of inverse monoids

John Meakin
1986 Journal of Pure and Applied Algebra  
Representations for the free rectangular band of inverse semigroups on a set and the free perfect rectangular band of inverse monoids on a set as quotients of suitable free unary semigroups are provided  ...  It is shown that every rectangular band of inverse semigroups may be embedded in a perfect rectangular band of inverse monoids and that the free rectangular band of inverse semigroups on a set Xmay be  ...  Acknowledgements I would like to thank Francis Pastijn and Mario Petrich for several useful conversations and suggestions concerning this paper.  ... 
doi:10.1016/0022-4049(86)90037-x fatcat:cjk6vdzoxbhtvastoi26glabc4

Page 4363 of Mathematical Reviews Vol. , Issue 85j [page]

1985 Mathematical Reviews  
Let = be a countable alphabet and &* the free semigroup generated by &.  ...  Further, we construct a semigroup 6,(S) and a homomorphism of S onto &(S) which induces the idempotent separating congruence yu, on S.  ... 
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