The weakest nontrivial idempotent equations

An equational condition is a set of equations in an algebraic language, and an algebraic structure satisfies such a condition if it possesses terms that meet the required equations. We find a single nontrivial equational condition which is implied by any nontrivial idempotent equational condition.

[1]  W. Taylor Varieties Obeying Homotopy Laws , 1977, Canadian Journal of Mathematics.

[2]  Stanley Burris,et al.  A course in universal algebra , 1981, Graduate texts in mathematics.

[3]  Walter Taylor,et al.  The Lattice of Interpretability Types of Varieties , 1984 .

[4]  R. McKenzie,et al.  Algebras, Lattices, Varieties , 1988 .

[5]  Some very weak identities , 1988 .

[6]  D. Hobby,et al.  The structure of finite algebras , 1988 .

[7]  Jaroslav Nesetril,et al.  On the complexity of H-coloring , 1990, J. Comb. Theory, Ser. B.

[8]  Non-covering in the interpretability lattice of equational theories , 1993 .

[9]  On the covering relation in the interpretability lattice of equational theories , 1993 .

[10]  Andrei A. Bulatov H-Coloring dichotomy revisited , 2005, Theor. Comput. Sci..

[11]  Peter Jeavons,et al.  Classifying the Complexity of Constraints Using Finite Algebras , 2005, SIAM J. Comput..

[12]  M. Maróti,et al.  Existence theorems for weakly symmetric operations , 2008 .

[13]  Manuel Bodirsky Constraint Satisfaction Problems with Infinite Templates , 2008, Complexity of Constraints.

[14]  Libor Barto,et al.  The CSP Dichotomy Holds for Digraphs with No Sources and No Sinks (A Positive Answer to a Conjecture of Bang-Jensen and Hell) , 2008, SIAM J. Comput..

[15]  M. Siggers A strong Mal’cev condition for locally finite varieties omitting the unary type , 2010 .

[16]  Libor Barto,et al.  Absorbing Subalgebras, Cyclic Terms, and the Constraint Satisfaction Problem , 2012, Log. Methods Comput. Sci..

[17]  Manuel Bodirsky,et al.  Complexity Classification in Infinite-Domain Constraint Satisfaction , 2012, ArXiv.

[18]  R. McKenzie,et al.  Optimal strong Mal’cev conditions for omitting type 1 in locally finite varieties , 2014 .

[19]  Libor Barto,et al.  THE CONSTRAINT SATISFACTION PROBLEM AND UNIVERSAL ALGEBRA , 2015, The Bulletin of Symbolic Logic.

[20]  Libor Barto,et al.  The algebraic dichotomy conjecture for infinite domain Constraint Satisfaction Problems , 2016, 2016 31st Annual ACM/IEEE Symposium on Logic in Computer Science (LICS).

[21]  Absorption in Universal Algebra and CSP , 2017, The Constraint Satisfaction Problem.

[22]  Michael Pinsker,et al.  PROJECTIVE CLONE HOMOMORPHISMS , 2014, The Journal of Symbolic Logic.