Araştırma Makalesi
BibTex RIS Kaynak Göster
Yıl 2020, Cilt: 2 Sayı: 1, 38 - 42, 30.04.2020

Öz

Kaynakça

  • [1] D. Busneag. Hilbert algebras with valuations. Math. Japon., 44 (2) (1996), 285–289.
  • [2] D. Busneag. On extensions of pseudo-valuations on Hilbert algebras. Discrete Math., 263 (1-3) (2003), 11–24.
  • [3] M. I. Doh and M. S. Kang. BCK/BCI-algebras with pseudo-valuation. Honam Math. J., 32 (2) (2010), 217–226.
  • [4] M. I. Doh and M. S. Kang, Commutative pseudo valuations on BCK-algebras. Int. J. Math. Math. Sci., Vol. 2011, Article ID 754047, 6 pages
  • [5] S. Ghorbani, Quotient BCI-algebras induced by pseudo-valuations. Iranian J. Math. Sci. Inf., 5 (2) (2010), 13–24.
  • [6] A. Iampan. A new branch of the logical algebra: UP-algebras. J. Algebra Relat Top., 5 (1) (2017), 35-–54.
  • [7] Y. B. Jun, S. S. Ahnamd E. H. Roh. BCC-algebras with pseudo-valuations. Filomat, 26 (2) (2012), 243-–252.
  • [8] Y. B. Jun, K. J. Lee and S. Z. Song. Quasi-valuation maps based on positive implicative ideals in BCK-algebras. Algebra and Discrete Mathematics, 26(1)(2018), 65-–75.
  • [9] A. N. A. Koam, A. Haider and M. A. Ansari. Pseudo-metric on KU-algebras. Korean J. Math., 27(1)(2019), 131–140.
  • [10] S. Mehrshad and N. Kouhestani. On pseudo-valuations on BCK-algebras. Filomat, 32(12)(2018), 4319-–4332.
  • [11] D. A. Romano. Proper UP-filters in UP-algebra. Universal J. Math. Appl., 1 (2) (2018), 98–100.
  • [12] D. A. Romano. Some properties of proper UP-filters of UP-algebras. Fund. J. Math. Appl., 1(2)(2018), 109–111.
  • [13] D. A. Romano. Notes on UP-ideals in UP-algebras. Comm. Adv. Math. Sci., 1 (1) (2018), 35–38.
  • [14] D. A. Romano. Pseudo-valuations on UP-algebras. Universal J. Math. Appl., 2 (3) (2019), 138-140.
  • [15] S.-Z. Song, E. H. Roh and Y. B. Jun. Quasi-valuation maps on BCK/BCI-algebras. Kyungpook Math. J., 55(4)(2015), 859–870.
  • [16] S.-Z. Song, H. Bordbar and Y. B. Jun. Quotient structures of BCK/BCI-algebras induced by quasi-valuation maps. Axioms 2018, 7(2): 26. 11 pages

A Construction of a Congruence in a UP-algebra by a Pseudo-valuation

Yıl 2020, Cilt: 2 Sayı: 1, 38 - 42, 30.04.2020

Öz

In our recently published paper, we study pseudo-valuations on UP-algebras
and obtain some related results. In this article, we use a pseudo-metric induced by a pseudo-valuation
to introduce a congruence relation on a UP-algebra. In addition, we construct
the quotient algebra induced by this relation and prove that it is also a UP-algebra.

Kaynakça

  • [1] D. Busneag. Hilbert algebras with valuations. Math. Japon., 44 (2) (1996), 285–289.
  • [2] D. Busneag. On extensions of pseudo-valuations on Hilbert algebras. Discrete Math., 263 (1-3) (2003), 11–24.
  • [3] M. I. Doh and M. S. Kang. BCK/BCI-algebras with pseudo-valuation. Honam Math. J., 32 (2) (2010), 217–226.
  • [4] M. I. Doh and M. S. Kang, Commutative pseudo valuations on BCK-algebras. Int. J. Math. Math. Sci., Vol. 2011, Article ID 754047, 6 pages
  • [5] S. Ghorbani, Quotient BCI-algebras induced by pseudo-valuations. Iranian J. Math. Sci. Inf., 5 (2) (2010), 13–24.
  • [6] A. Iampan. A new branch of the logical algebra: UP-algebras. J. Algebra Relat Top., 5 (1) (2017), 35-–54.
  • [7] Y. B. Jun, S. S. Ahnamd E. H. Roh. BCC-algebras with pseudo-valuations. Filomat, 26 (2) (2012), 243-–252.
  • [8] Y. B. Jun, K. J. Lee and S. Z. Song. Quasi-valuation maps based on positive implicative ideals in BCK-algebras. Algebra and Discrete Mathematics, 26(1)(2018), 65-–75.
  • [9] A. N. A. Koam, A. Haider and M. A. Ansari. Pseudo-metric on KU-algebras. Korean J. Math., 27(1)(2019), 131–140.
  • [10] S. Mehrshad and N. Kouhestani. On pseudo-valuations on BCK-algebras. Filomat, 32(12)(2018), 4319-–4332.
  • [11] D. A. Romano. Proper UP-filters in UP-algebra. Universal J. Math. Appl., 1 (2) (2018), 98–100.
  • [12] D. A. Romano. Some properties of proper UP-filters of UP-algebras. Fund. J. Math. Appl., 1(2)(2018), 109–111.
  • [13] D. A. Romano. Notes on UP-ideals in UP-algebras. Comm. Adv. Math. Sci., 1 (1) (2018), 35–38.
  • [14] D. A. Romano. Pseudo-valuations on UP-algebras. Universal J. Math. Appl., 2 (3) (2019), 138-140.
  • [15] S.-Z. Song, E. H. Roh and Y. B. Jun. Quasi-valuation maps on BCK/BCI-algebras. Kyungpook Math. J., 55(4)(2015), 859–870.
  • [16] S.-Z. Song, H. Bordbar and Y. B. Jun. Quotient structures of BCK/BCI-algebras induced by quasi-valuation maps. Axioms 2018, 7(2): 26. 11 pages
Toplam 16 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Articles
Yazarlar

Daniel A. Romano 0000-0003-1148-3258

Yayımlanma Tarihi 30 Nisan 2020
Kabul Tarihi 29 Nisan 2020
Yayımlandığı Sayı Yıl 2020 Cilt: 2 Sayı: 1

Kaynak Göster

APA Romano, D. A. (2020). A Construction of a Congruence in a UP-algebra by a Pseudo-valuation. Maltepe Journal of Mathematics, 2(1), 38-42.
AMA Romano DA. A Construction of a Congruence in a UP-algebra by a Pseudo-valuation. Maltepe Journal of Mathematics. Nisan 2020;2(1):38-42.
Chicago Romano, Daniel A. “A Construction of a Congruence in a UP-Algebra by a Pseudo-Valuation”. Maltepe Journal of Mathematics 2, sy. 1 (Nisan 2020): 38-42.
EndNote Romano DA (01 Nisan 2020) A Construction of a Congruence in a UP-algebra by a Pseudo-valuation. Maltepe Journal of Mathematics 2 1 38–42.
IEEE D. A. Romano, “A Construction of a Congruence in a UP-algebra by a Pseudo-valuation”, Maltepe Journal of Mathematics, c. 2, sy. 1, ss. 38–42, 2020.
ISNAD Romano, Daniel A. “A Construction of a Congruence in a UP-Algebra by a Pseudo-Valuation”. Maltepe Journal of Mathematics 2/1 (Nisan 2020), 38-42.
JAMA Romano DA. A Construction of a Congruence in a UP-algebra by a Pseudo-valuation. Maltepe Journal of Mathematics. 2020;2:38–42.
MLA Romano, Daniel A. “A Construction of a Congruence in a UP-Algebra by a Pseudo-Valuation”. Maltepe Journal of Mathematics, c. 2, sy. 1, 2020, ss. 38-42.
Vancouver Romano DA. A Construction of a Congruence in a UP-algebra by a Pseudo-valuation. Maltepe Journal of Mathematics. 2020;2(1):38-42.

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