A. Shimshon, A. , and J. Levitzki, Minimal identities for algebras, Proc. Amer. Math. Soc, vol.112, pp.449-463, 1950.

G. Robert, S. Burns, and . Oates-williams, Varieties of groups and normal-subgroup lattices?a survey, Algebra Universalis, vol.32, issue.1, pp.145-152, 1994.

S. Burris and H. P. Sankappanavar, A Course in Universal Algebra, Graduate Texts in Mathematics, vol.78, 1981.
DOI : 10.1007/978-1-4613-8130-3

R. Freese and F. Planar-sublattices-of, Algebra Universalis Alan Day's early work: congruence identities, Algebra Universalis, vol.3497, issue.4 6 1 1, pp.69-72, 1976.

M. Haiman, Proof theory for linear lattices, Advances in Mathematics, vol.58, issue.3, pp.209-242, 1985.
DOI : 10.1016/0001-8708(85)90118-5

J. M. Howie, An Introduction to Semigroup Theory, 1976.

B. Jónsson, On the representation of lattices The class of Arguesian lattices is self-dual, Math. Scand, vol.115, issue.2, pp.193-206, 1953.

G. Kudryavtseva, M. V. Lawson, D. H. Lenz, and P. Resende, Invariant means on Boolean inverse monoids, Semigroup Forum, vol.34, issue.2, pp.77-101, 2016.
DOI : 10.1007/s00233-015-9768-3

V. Mark, I. Lawson, and . Semigroups, The theory of partial symmetries) [15] , A noncommutative generalization of Stone duality) [16] , Non-commutative Stone duality: inverse semigroups, topological groupoids and C * algebras, MR 1694900, pp.385-404, 1998.

V. Mark, D. H. Lawson, and . Lenz, Pseudogroups and theirétaletheirétale groupoids, Adv. Math, vol.244, pp.117-170, 2013.

V. Mark, P. Lawson, and . Scott, AF inverse monoids and the structure of countable MValgebras, J. Pure Appl. Algebra, vol.221, issue.1, pp.45-74, 2017.

R. N. Mckenzie, G. F. Mcnulty, and W. F. Taylor, Algebras, Lattices, Varieties The Wadsworth & Brooks, Cole Mathematics Series, vol.88, p.88364408001, 1987.

C. C. John and . Mckinsey, The decision problem for some classes of sentences without quantifiers, J. Symbolic Logic, vol.8, pp.61-76, 1943.

D. Walter and . Munn, Free inverse semigroups, Proc. London Math. Soc. (3), pp.385-404, 1974.

H. Neumann, Varieties of Groups, 1967.

A. Ju, ?. Ol, and . Sanski?-i, The finite basis problem for identities in groups, Izv. Akad. Nauk SSSR Ser. Mat, vol.34, pp.376-384, 1970.

R. Norman and . Reilly, Varieties of completely semisimple inverse semigroups, J. Algebra, vol.65, issue.2, pp.427-444, 1980.

A. Tarski and C. Algebras, With an Appendix: Cardinal Products of Isomorphism Types, p.29954, 1949.

R. Alistair and . Wallis, Semigroup and category-theoretic approaches to partial symmetry

F. Wehrung, The dimension monoid of a lattice, Algebra Universalis, vol.40, issue.3, pp.247-411, 1998.
DOI : 10.1007/s000120050091

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