The Globals of Some Subpseudovarieties of DA

Let be the pseudovariety of all finite monoids whose principal right ideals have a unique generator, let be its dual, and let . Using the word problem for free pro- monoids, it is shown that the bilateral semidirect product is local, where denotes the pseudovariety of all finite semilattices. The global of the pseudovariety where is also computed and it is shown that this join is not local.

[1]  Peter R. Jones.  Monoid varieties defined byxn+1=x are local , 1993 .

[2]  Jorge Almeida,et al.  On finitely based pseudovarieties of the forms V ∗ D and V ∗ Dn , 2000 .

[3]  Peter R. Jones.  Profinite categories, implicit operations and pseudovarieties of categories , 1996 .

[4]  Pascal Weil,et al.  Decomposition techniques for finite semigroups, using categories II , 1989 .

[5]  Jorge Almeida,et al.  Finite Semigroups and Universal Algebra , 1995 .

[6]  Pascal Weil,et al.  Profinite categories and semidirect products , 1998 .

[7]  Bret Tilson,et al.  Categories as algebra: An essential ingredient in the theory of monoids , 1987 .

[8]  Jan Reiterman,et al.  The Birkhoff theorem for finite algebras , 1982 .

[9]  Janusz A. Brzozowski,et al.  Characterizations of locally testable events , 1973, Discret. Math..

[10]  Imre Simon,et al.  Piecewise testable events , 1975, Automata Theory and Formal Languages.

[11]  Jorge Almeida,et al.  The join of the pseudovarieties of R-trivial and L-trivial monoids , 1989 .

[12]  Jorge Almeida.  FINITE SEMIGROUPS: AN INTRODUCTION TO A UNIFIED THEORY OF PSEUDOVARIETIES , 2002 .

[13]  Benjamin Steinberg.  SEMIDIRECT PRODUCTS OF CATEGORIES AND APPLICATIONS , 1999 .

[14]  Peter R. Jones,et al.  Locality of DS and associated varieties , 1995 .

[15]  Jorge Almeida.  A Syntactical Proof of Locality of da , 1996, Int. J. Algebra Comput..

[16]  Price E. Stiffler,et al.  Chapter 1. Extension of the fundamental theorem of finite semigroups , 1973 .

[17]  Pascal Weil,et al.  Profinite Methods in Semigroup Theory , 2002, Int. J. Algebra Comput..

[18]  Jean-Éric Pin.  Hiérarchies de Concaténation , 1984, RAIRO Theor. Informatics Appl..

[19]  Pascal Weil,et al.  Relatively Free Profinite Monoids: An Introduction and Examples , 1995 .

[20]  Samuel Eilenberg,et al.  Automata, languages, and machines. A , 1974, Pure and applied mathematics.

[21]  On the equation V*G=EV , 2002 .

[22]  Berndt Farwer,et al.  ω-automata , 2002 .

[23]  Jorge Almeida,et al.  On regular implicit operations , 1993 .

[24]  Lawrence S. Kroll.  Mathematica--A System for Doing Mathematics by Computer. , 1989 .

[25]  Robert Knast.  Some Theorems on Graph Congruences , 1983, RAIRO Theor. Informatics Appl..

[26]  Pascal Weil,et al.  Closure of Varieties of Languages under Products with Counter , 1992, J. Comput. Syst. Sci..

[27]  Howard Straubing,et al.  Monoids of upper-triangular matrices , 1981 .

[28]  John Rhodes,et al.  The kernel of monoid morphisms , 1989 .