{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,29]],"date-time":"2025-09-29T11:46:24Z","timestamp":1759146384243},"reference-count":20,"publisher":"World Scientific Pub Co Pte Ltd","issue":"04","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Algebra Comput."],"published-print":{"date-parts":[[2022,6]]},"abstract":"<jats:p> A variety is primitive if every subquasivariety is equational, i.e. a subvariety. In this paper, we explore the connection between primitive lattice varieties and Whitman\u2019s condition (W). For example, if every finite subdirectly irreducible lattice in a locally finite variety [Formula: see text] satisfies Whitman\u2019s condition (W), then [Formula: see text] is primitive. This allows us to construct infinitely many sequences of primitive lattice varieties, and to show that there are [Formula: see text] such varieties. Some lattices that fail (W) also generate primitive varieties. But if I is a (W)-failure interval in a finite subdirectly irreducible lattice [Formula: see text], and [Formula: see text] denotes the lattice with I doubled, then [Formula: see text] is never primitive. <\/jats:p>","DOI":"10.1142\/s021819672250031x","type":"journal-article","created":{"date-parts":[[2022,3,29]],"date-time":"2022-03-29T07:36:07Z","timestamp":1648539367000},"page":"717-752","source":"Crossref","is-referenced-by-count":2,"title":["Primitive lattice varieties"],"prefix":"10.1142","volume":"32","author":[{"given":"Peter","family":"Jipsen","sequence":"first","affiliation":[{"name":"Department of Mathematics, Chapman University, Orange, CA 92866, USA"}]},{"given":"J. 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