{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,9,4]],"date-time":"2024-09-04T20:57:11Z","timestamp":1725483431754},"reference-count":0,"publisher":"EasyChair","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"abstract":"<jats:p>Using Vaggione's concept of central element in a double pointed algebra, we<\/jats:p><jats:p>introduce the notion of Boolean like variety as a generalisation of<\/jats:p><jats:p>Boolean algebras to an arbitrary similarity type. Appropriately relaxing the<\/jats:p><jats:p>requirement that every element be central in any member of the variety, we<\/jats:p><jats:p>obtain the more general class of semi-Boolean like varieties, which<\/jats:p><jats:p>still retain many of the pleasing properties of Boolean algebras. We prove<\/jats:p><jats:p>that a double pointed variety is discriminator iff it is semi-Boolean like,<\/jats:p><jats:p>idempotent, and 0-regular. This theorem yields a new Maltsev-style<\/jats:p><jats:p>characterisation of double pointed discriminator varieties.<\/jats:p><jats:p>Moreover, we point out the exact relationship between semi-Boolean-like<\/jats:p><jats:p>varieties and the quasi-discriminator varieties, and we provide<\/jats:p><jats:p>semi-Boolean-like algebras with an explicit weak Boolean product<\/jats:p><jats:p>representation with directly indecomposable factors. Finally, we discuss idempotent<\/jats:p><jats:p>semi-Boolean-like algebras. We consider a noncommutative generalisation of Boolean algebras and prove - along the lines of similar results available for pointed discriminator varieties or for varieties with a commutative ternary deduction term that every idempotent semi-Boolean-like variety is term equivalent to a variety of noncommutative Boolean algebras with additional operations.<\/jats:p>","DOI":"10.29007\/dzwk","type":"proceedings-article","created":{"date-parts":[[2018,1,23]],"date-time":"2018-01-23T22:59:06Z","timestamp":1516748346000},"page":"141-136","source":"Crossref","is-referenced-by-count":0,"title":["Boolean like algebras"],"prefix":"10.29007","volume":"25","author":[{"given":"Antonio","family":"Ledda","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Tomasz","family":"Kowalski","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Francesco","family":"Paoli","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Antonino","family":"Salibra","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"11545","event":{"name":"TACL 2013. Sixth International Conference on Topology, Algebra and Categories in Logic"},"container-title":["EPiC Series in Computing"],"original-title":[],"deposited":{"date-parts":[[2018,1,23]],"date-time":"2018-01-23T23:01:12Z","timestamp":1516748472000},"score":1,"resource":{"primary":{"URL":"https:\/\/easychair.org\/publications\/paper\/1S"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[null]]},"references-count":0,"URL":"https:\/\/doi.org\/10.29007\/dzwk","relation":{},"ISSN":["2398-7340"],"issn-type":[{"type":"print","value":"2398-7340"}],"subject":[]}}