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INTERVAL SHEFFER STROKE BASIC ALGEBRAS

Yıl 2019, Cilt: 9 Sayı: 1, 134 - 141, 01.03.2019

Öz

In this paper we deal with She er stroke basic algebras A = A; j , and we de ne the operations ja, jb, jb a for any elements a; b 2 A in such a way that [a; 1]; ja , [0; b]; jb , [a; b]; jb a become also She er Stroke basic algebras, respectively. Subsequeutly, we show that these interval She er Stroke basic algebras on a given She er Stroke basic algebra A = A; j verify the patchwork condition.

Kaynakça

  • I. Chajda, (2015), Basic algebras, logics, trends and applications, Asian-European Journal of Mathe- matics 8.03, 1550040.
  • I. Chajda, (2005), Sheffer operation in ortholattices, Acta Universitatis Palackianae Olomucensis, Fac- ultas Rerum Naturalium, Mathematica, 44.1, 19-23.
  • I. Chajda, R. Halaˇs, and J. K¨uhr, (2007), Semilattice structures, Vol. 30, Heldermann Verlag, Lemgo, Germany.
  • I. Chajda, and M. Kolaˇr´ık, (2009), Independence of the axiomatic system of basic algebras, Soft Computing 13, 41-43.
  • I. Chajda, and M. Kolaˇr´ık, (2009), Interval Basic Algebras, NOVI SAD J. MATH., Vol. 39-2.
  • I. Chajda, and J. K¨uhr, (2006), A note on interval MV-algebras, Math. Slovaca, 56, 47-52.
  • I. Chajda, and J. K¨uhr, (2006), GMV-algebras and meet-semilattices with sectionally antitone permu- tations, Math. Slovaca, 56, 275-288
  • A. Dvureˇcenskij, and M. Hyˇc ko, (2006), Algebras on subintervals of BL-algebras, pseudo BL-algebras and bounded residuated l-monoids, Math. Slovaca, 56, 125-144.
  • J. Jakubik, (2006), On intervals and the dual of pseudo MV-algebras, Math. Slovaca, 56, 213-221.
  • H. M. Sheffer, (1913), A set of five independent postulates for Boolean algebras, with application to logical constants, Transactions of the American Mathematical Society, 14(4), 481-488.
  • Oner T., Senturk I., (2017), The Sheffer Stroke Operation Reducts of Basic Algebras, Open Math., 15, 926-935.
  • McCune, William, et al., (2002), Short single axioms for Boolean algebra, Journal of Automated Reasoning, 29.1, 1-16.
  • Abbott J. C., (1967), Implicational algebras, Bulletin math´ematique de la Soci´et´e des Sciences Math´ematiques de la R´epublique Socialiste de Roumanie, 11.1, 3-23.
Yıl 2019, Cilt: 9 Sayı: 1, 134 - 141, 01.03.2019

Öz

Kaynakça

  • I. Chajda, (2015), Basic algebras, logics, trends and applications, Asian-European Journal of Mathe- matics 8.03, 1550040.
  • I. Chajda, (2005), Sheffer operation in ortholattices, Acta Universitatis Palackianae Olomucensis, Fac- ultas Rerum Naturalium, Mathematica, 44.1, 19-23.
  • I. Chajda, R. Halaˇs, and J. K¨uhr, (2007), Semilattice structures, Vol. 30, Heldermann Verlag, Lemgo, Germany.
  • I. Chajda, and M. Kolaˇr´ık, (2009), Independence of the axiomatic system of basic algebras, Soft Computing 13, 41-43.
  • I. Chajda, and M. Kolaˇr´ık, (2009), Interval Basic Algebras, NOVI SAD J. MATH., Vol. 39-2.
  • I. Chajda, and J. K¨uhr, (2006), A note on interval MV-algebras, Math. Slovaca, 56, 47-52.
  • I. Chajda, and J. K¨uhr, (2006), GMV-algebras and meet-semilattices with sectionally antitone permu- tations, Math. Slovaca, 56, 275-288
  • A. Dvureˇcenskij, and M. Hyˇc ko, (2006), Algebras on subintervals of BL-algebras, pseudo BL-algebras and bounded residuated l-monoids, Math. Slovaca, 56, 125-144.
  • J. Jakubik, (2006), On intervals and the dual of pseudo MV-algebras, Math. Slovaca, 56, 213-221.
  • H. M. Sheffer, (1913), A set of five independent postulates for Boolean algebras, with application to logical constants, Transactions of the American Mathematical Society, 14(4), 481-488.
  • Oner T., Senturk I., (2017), The Sheffer Stroke Operation Reducts of Basic Algebras, Open Math., 15, 926-935.
  • McCune, William, et al., (2002), Short single axioms for Boolean algebra, Journal of Automated Reasoning, 29.1, 1-16.
  • Abbott J. C., (1967), Implicational algebras, Bulletin math´ematique de la Soci´et´e des Sciences Math´ematiques de la R´epublique Socialiste de Roumanie, 11.1, 3-23.
Toplam 13 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Bölüm Research Article
Yazarlar

T. Oner Bu kişi benim

T. Katıcan Bu kişi benim

A. Ülker Bu kişi benim

Yayımlanma Tarihi 1 Mart 2019
Yayımlandığı Sayı Yıl 2019 Cilt: 9 Sayı: 1

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