Department of Mathematics
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During the mid 1980's we developed an ad hoc method to find all identities common to two given group terms (or loop terms). In this talk, we recall that technique and apply that idea to find equational bases for the lattice join of some familiar equational theories. This research was done in collaboration with George Grätzer, David Kelly, Barry Wolk, R.W. Quackenbush and William McCune.

References:

1. Grätzer, G.; Padmanabhan, R,; Symmetric difference in abelian groups, Pacific J. Math. 2 74 (1978), 339–347.
2. Kelly, David; Padmanabhan, R.; Wolk, B.; Identities common to addition and subtraction, Houston J. Math. 2 11 (1985), no. 3, 335–343.
3. Kelly, David; Padmanabhan, R.; Identities common to four abelian group operations with zero, Algebra Universalis 21 2 (1985), 1–24.
4. McCune, W; Padmanabhan, R.; Symmetric difference in commutative Moufang loops, (to appear).
5. Padmanabhan, R; Quackenbush, R. W.; Equational theories of algebras with distributive congruences, Proc. AMS 11(2) 1973 373–377.