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Boolean algebra (structure)
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== References == {{reflist|30em}} ===Works cited=== *{{cite book |first1=B.A. |last1=Davey |author2link = Hilary Priestley|first2=H.A. |last2=Priestley | title=Introduction to Lattices and Order | title-link= Introduction to Lattices and Order | year=1990 | publisher=Cambridge University Press | series=Cambridge Mathematical Textbooks}} *{{citation|title=Basic Algebra: Groups, Rings, and Fields|first=Paul M.|last=Cohn|publisher= Springer |year=2003 |isbn=9781852335878 |pages=51, 70–81 |author-link=Paul Cohn}} *{{citation | last1 = Givant | first1 = Steven | first2 = Paul | last2 = Halmos |author2link = Paul Halmos | year = 2009 | title = Introduction to Boolean Algebras | series = [[Undergraduate Texts in Mathematics]] | publisher = [[Springer Science+Business Media|Springer]] | isbn = 978-0-387-40293-2}}. *{{citation|title=Boolean Algebra|first=R. L.|last=Goodstein|authorlink = Reuben Goodstein|publisher=Courier Dover Publications|year=2012|isbn=9780486154978|chapter=Chapter 2: The self-dual system of axioms|pages=21ff|chapter-url=https://books.google.com/books?id=0fxW2KiyxWwC&pg=PA21}} *{{cite journal | last1=Hsiang | first1=Jieh | title=Refutational Theorem Proving Using Term Rewriting Systems | journal= [[Artificial Intelligence (journal)|Artificial Intelligence]] | year=1985 | volume=25 | issue=3 | pages=255–300 | url=https://www.researchgate.net/publication/223327412 | doi=10.1016/0004-3702(85)90074-8 }} *{{cite journal | author-link=Edward V. Huntington | first1=Edward V. | last1=Huntington | title=Sets of Independent Postulates for the Algebra of Logic | journal=[[Transactions of the American Mathematical Society]] | year=1904 | volume=5 | issue=3 | pages=288–309 | jstor=1986459 | doi=10.1090/s0002-9947-1904-1500675-4| url=https://zenodo.org/record/1431563 | doi-access=free }} *{{citation | last1 = Padmanabhan | first1 = Ranganathan | last2 = Rudeanu | first2 = Sergiu | year = 2008 | title = Axioms for lattices and boolean algebras | publisher = World Scientific | isbn = 978-981-283-454-6}}. *{{cite journal | author-link=Marshall H. Stone | first1=Marshall H. | last1=Stone | title=The Theory of Representations for Boolean Algebra | journal=[[Transactions of the American Mathematical Society]] | year=1936 | volume=40 | pages=37–111 | doi=10.1090/s0002-9947-1936-1501865-8| doi-access=free }} *{{cite book | author-link=A.N. Whitehead | first1=A.N. | last1=Whitehead | title=A Treatise on Universal Algebra | year=1898 | publisher=Cambridge University Press | isbn=978-1-4297-0032-0 | url=http://projecteuclid.org/euclid.chmm/1263316509}} === General references === {{more footnotes needed|date=July 2013}} *{{citation | last1 = Brown | first1 = Stephen | last2 = Vranesic | first2 = Zvonko | year = 2002 | title = Fundamentals of Digital Logic with VHDL Design | edition = 2nd | publisher = [[McGraw-Hill|McGraw–Hill]] | isbn = 978-0-07-249938-4}}. See Section 2.5. *{{cite journal |first1=A. |last1=Boudet |first2=J.P. |last2=Jouannaud |first3=M. |last3=Schmidt-Schauß | title=Unification in Boolean Rings and Abelian Groups | journal=[[Journal of Symbolic Computation]] | year=1989 | volume=8 |issue=5 | pages=449–477 | doi=10.1016/s0747-7171(89)80054-9|doi-access=free }} *{{citation | last1 = Cori | first1 = Rene | last2 = Lascar | first2 = Daniel | year = 2000 | title = Mathematical Logic: A Course with Exercises | publisher = [[Oxford University Press]] | isbn = 978-0-19-850048-3}}. See Chapter 2. *{{citation | last = Dahn | first = B. I. | year = 1998 | title = Robbins Algebras are Boolean: A Revision of McCune's Computer-Generated Solution of the Robbins Problem | journal = [[Journal of Algebra]] | volume = 208 | pages = 526–532 | doi = 10.1006/jabr.1998.7467 | issue = 2| doi-access = free }}. *{{citation | author-link = Paul Halmos | last = Halmos | first = Paul | year = 1963 | title = Lectures on Boolean Algebras | publisher = Van Nostrand | isbn = 978-0-387-90094-0}}. *{{citation | author-link1 = Paul Halmos | last1 = Halmos | first1 = Paul | first2 = Steven | last2 = Givant | year = 1998 | title = Logic as Algebra | series = Dolciani Mathematical Expositions | volume = 21 | publisher = [[Mathematical Association of America]] | isbn = 978-0-88385-327-6 | url-access = registration | url = https://archive.org/details/logicasalgebra0000halm }}. *{{citation | author-link = Edward Vermilye Huntington | last = Huntington | first = E. V. | year = 1933a | title = New sets of independent postulates for the algebra of logic | journal = [[Transactions of the American Mathematical Society]] | volume = 35 | pages = 274–304 | doi = 10.2307/1989325 | issue = 1 | publisher = American Mathematical Society | url = https://www.ams.org/journals/tran/1933-035-01/S0002-9947-1933-1501684-X/S0002-9947-1933-1501684-X.pdf | jstor = 1989325}}. *{{citation | author-link = Edward Vermilye Huntington | last = Huntington | first = E. V. | year = 1933b | title = Boolean algebra: A correction | journal = [[Transactions of the American Mathematical Society]] | volume = 35 | pages = 557–558 | doi = 10.2307/1989783 | issue = 2 | jstor = 1989783}} *{{citation | last = Mendelson | first = Elliott | year = 1970 | title = Boolean Algebra and Switching Circuits | series = Schaum's Outline Series in Mathematics | publisher = [[McGraw-Hill|McGraw–Hill]] | isbn = 978-0-07-041460-0 | url-access = registration | url = https://archive.org/details/schaumsoutlineof00mend }} *{{citation | editor1-last = Monk | editor1-first = J. Donald | editor2-first = R. | editor2-last = Bonnet | year = 1989 | title = Handbook of Boolean Algebras | publisher = [[Elsevier|North-Holland]] | isbn = 978-0-444-87291-3 | url-access = registration | url = https://archive.org/details/handbookofboolea0000unse }}. In 3 volumes. (Vol.1:{{ISBN|978-0-444-70261-6}}, Vol.2:{{ISBN|978-0-444-87152-7}}, Vol.3:{{ISBN|978-0-444-87153-4}}) *{{citation | author-link = Roman Sikorski | last = Sikorski | first = Roman | year = 1966 | title = Boolean Algebras | series = Ergebnisse der Mathematik und ihrer Grenzgebiete | publisher = [[Springer Verlag]] | ref = Sikorski1966BooleanAlgebras }}. *{{citation | last = Stoll | first = R. R. | year = 1963 | title = Set Theory and Logic | publisher = W. H. Freeman | isbn = 978-0-486-63829-4}}. Reprinted by [[Dover Publications]], 1979.
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