1. Introduction. J. Berman [2] initiated the study of a variety % of bounded distributive lattices endowed with a dual homomorphic operation paying particular attention to certain subvarieties JC m , n . Subsequently, A. Urquhart [8] named the algebras in 3C distributive Ockham algebras, and developed a duality theory, based on H. A. Priestley's order-topological duality for bounded distributive lattices [6], [7]. Amongst other things, Urquhart described the ordered spaces dual to the

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... y irreducible algebras in Sif. This work was developed further still by M. S. Goldberg in his thesis and the paper [5]. Recently, T. S. Blyth and J. C. Varlet [3], in abstracting de Morgan and Stone algebras, studied a subvariety MS of the variety 3Sf ltl . The main result in [3] is that there are, up to isomorphism, nine subdirectly irreducible algebras in MS and their Hasse diagrams are exhibited. The methods employed in [3] are purely algebraic and can be generalized to show that, up to isomorphism, there are twenty subdirectly irreducible algebras in 3ST 1>: 1 . In section 3 of this paper, we take a short cut to this result by utilizing the results of Urquhart and Goldberg. Our basic method is simple: the results of Goldberg [5] are applied to 3if lfl to produce a certain eight-element algebra B x in 9ifi F i, whose lattice reduct is Boolean and whose subalgebras are, up to isomorphism, precisely the subdirectly irreducibles in 3K 11 . We then pick out of the list of twenty such algebras those belonging to the variety MS. In section 4, we sketch a purely algebraic proof along the lines followed by Blyth and Varlet in [3]. Preliminaries. A distributive Ockham algebra is an algebra (L, v, A, °, 0,1) of type (2, 2,1,0, 0) such that (L, v, A, 0,1) is a bounded distributive lattice and ° is a unary operation denned on L such that, for all x, y e L, Glasgow Math. J. 25 (1984) 175-181. https://www.cambridge.org/core/terms. https://doi.