{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,9,26]],"date-time":"2023-09-26T08:13:25Z","timestamp":1695716005467},"reference-count":9,"publisher":"Wiley","issue":"4-5","license":[{"start":{"date-parts":[[2012,6,13]],"date-time":"2012-06-13T00:00:00Z","timestamp":1339545600000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Mathematical Logic Qtrly"],"published-print":{"date-parts":[[2012,8]]},"abstract":"Abstract<\/jats:title>For a Peirce algebra \\documentclass{article}\\usepackage{amssymb}\\begin{document}\\pagestyle{empty}${\\mathcal P}$\\end{document}<\/jats:styled-content>, lattices \\documentclass{article}\\usepackage{amssymb}\\begin{document}\\pagestyle{empty}$\\mathrm{Cong}\\mathcal {P}$\\end{document}<\/jats:styled-content> of all heterogenous Peirce congruences and \\documentclass{article}\\usepackage{amssymb}\\begin{document}\\pagestyle{empty}$\\mathrm{Ide}\\mathcal {P}$\\end{document}<\/jats:styled-content> of all heterogenous Peirce ideals are presented. The notions of kernel of a Peirce congruence and the congruence induced by a Peirce ideal are introduced to describe an isomorphism between \\documentclass{article}\\usepackage{amssymb}\\begin{document}\\pagestyle{empty}$\\mathrm{Cong}\\mathcal {P}$\\end{document}<\/jats:styled-content> and \\documentclass{article}\\usepackage{amssymb}\\begin{document}\\pagestyle{empty}$\\mathrm{Ide}\\mathcal {P}$\\end{document}<\/jats:styled-content>. This isomorphism leads us to conclude that the class of the Peirce algebras is ideal determined. Opposed to Boolean modules case, each part of a Peirce ideal I<\/jats:italic> = (I<\/jats:italic>1<\/jats:sub>, I<\/jats:italic>2<\/jats:sub>) determines the other one. A similar result is valid to Peirce congruences. A characterization of the simple Peirce algebras is presented coinciding to that given by Brink, Britz and Schmidt in a homogeneous approach.<\/jats:p>","DOI":"10.1002\/malq.201020058","type":"journal-article","created":{"date-parts":[[2012,8,3]],"date-time":"2012-08-03T18:27:13Z","timestamp":1344018433000},"page":"252-262","source":"Crossref","is-referenced-by-count":1,"title":["Congruences and ideals on Peirce algebras: a heterogeneous\/homogeneous point of view"],"prefix":"10.1002","volume":"58","author":[{"given":"Sandra Marques","family":"Pinto","sequence":"first","affiliation":[]},{"given":"M. Teresa","family":"Oliveira\u2010Martins","sequence":"additional","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2012,6,13]]},"reference":[{"key":"e_1_2_9_2_1","first-page":"291","article-title":"Boolean Modules","volume":"71","author":"Brink C.","year":"1981","journal-title":"Boolean Modules"},{"key":"e_1_2_9_3_1","first-page":"339","article-title":"Peirce Algebras","volume":"6","author":"Brink C.","year":"1994","journal-title":"Peirce Algebras"},{"key":"e_1_2_9_4_1","first-page":"341","article-title":"Distributive and modular laws in the arithmetic of relation algebras","volume":"1","author":"Chin L. H.","year":"1951","journal-title":"Distributive and modular laws in the arithmetic of relation algebras"},{"key":"e_1_2_9_5_1","volume-title":"General lattices theory","author":"Gr\u00e4tzer G.","year":"1998"},{"key":"e_1_2_9_6_1","doi-asserted-by":"publisher","DOI":"10.1007\/BF01191491"},{"issue":"6","key":"e_1_2_9_7_1","first-page":"571","article-title":"Congruences and ideals on Boolean modules: a heterogeneous point of view","volume":"57","author":"Pinto S. M.","year":"2011","journal-title":"Congruences and ideals on Boolean modules: a heterogeneous point of view"},{"key":"e_1_2_9_8_1","first-page":"134","article-title":"Monadic Dynamic Algebras","volume":"52","author":"Pinto S. M.","year":"2006","journal-title":"Monadic Dynamic Algebras"},{"key":"e_1_2_9_9_1","first-page":"571","article-title":"Dynamic algebras: examples","volume":"55","author":"Pratt V. R.","year":"1992","journal-title":"Dynamic algebras: examples"},{"key":"e_1_2_9_10_1","first-page":"73","article-title":"On the calculus of relations","volume":"6","author":"Tarski A.","year":"1941","journal-title":"On the calculus of relations"}],"container-title":["Mathematical Logic Quarterly"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fmalq.201020058","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fmalq.201020058","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/malq.201020058","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,8,31]],"date-time":"2023-08-31T03:38:53Z","timestamp":1693453133000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/malq.201020058"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2012,6,13]]},"references-count":9,"journal-issue":{"issue":"4-5","published-print":{"date-parts":[[2012,8]]}},"alternative-id":["10.1002\/malq.201020058"],"URL":"https:\/\/doi.org\/10.1002\/malq.201020058","archive":["Portico"],"relation":{},"ISSN":["0942-5616","1521-3870"],"issn-type":[{"value":"0942-5616","type":"print"},{"value":"1521-3870","type":"electronic"}],"subject":[],"published":{"date-parts":[[2012,6,13]]}}}