Research Article
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Pseudo-Valuations on UP-Algebras

Year 2019, Volume: 2 Issue: 3, 138 - 140, 30.09.2019

Daniel A. Romano

https://doi.org/10.32323/ujma.556269
Cited By: 1

Abstract

Looking at pseudo-valuations on some classes of abstract algebras, such as BCK, BCI, BCC and KU, in this article we introduce the concept of pseudo-valuations on UP-algebras and analyze the relationship of these mappings with UP-substructures.

Keywords

UP-algebra UP-ideal proper UP-filter

References

  • [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. Sc. Inform., 5(2010), 13–24.
  • [6] A. Iampan. A new branch of the universal algebra: UP-algebras. Journal of Algebra and Related Topics, 5(1)(2017), 35–54.
  • [7] Y. B. Jun, S. S. Ahn amd 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 Journal of Mathematics and Applications, 1(2)(2018), 98–100.
  • [12] 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.
  • [13] 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. 11pages

Year 2019, Volume: 2 Issue: 3, 138 - 140, 30.09.2019

Daniel A. Romano

https://doi.org/10.32323/ujma.556269
Cited By: 1

Abstract

References

  • [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. Sc. Inform., 5(2010), 13–24.
  • [6] A. Iampan. A new branch of the universal algebra: UP-algebras. Journal of Algebra and Related Topics, 5(1)(2017), 35–54.
  • [7] Y. B. Jun, S. S. Ahn amd 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 Journal of Mathematics and Applications, 1(2)(2018), 98–100.
  • [12] 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.
  • [13] 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. 11pages
There are 13 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Research Article
Authors

Daniel A. Romano 0000-0003-1148-3258

Submission Date April 19, 2019
Acceptance Date September 6, 2019
Publication Date September 30, 2019
Published in Issue Year 2019 Volume: 2 Issue: 3

Cite

APA Romano, D. A. (2019). Pseudo-Valuations on UP-Algebras. Universal Journal of Mathematics and Applications, 2(3), 138-140. https://doi.org/10.32323/ujma.556269
AMA Romano DA. Pseudo-Valuations on UP-Algebras. Univ. J. Math. Appl. September 2019;2(3):138-140. doi:10.32323/ujma.556269
Chicago Romano, Daniel A. “Pseudo-Valuations on UP-Algebras”. Universal Journal of Mathematics and Applications 2, no. 3 (September 2019): 138-40. https://doi.org/10.32323/ujma.556269.
EndNote Romano DA (September 1, 2019) Pseudo-Valuations on UP-Algebras. Universal Journal of Mathematics and Applications 2 3 138–140.
IEEE D. A. Romano, “Pseudo-Valuations on UP-Algebras”, Univ. J. Math. Appl., vol. 2, no. 3, pp. 138–140, 2019, doi: 10.32323/ujma.556269.
ISNAD Romano, Daniel A. “Pseudo-Valuations on UP-Algebras”. Universal Journal of Mathematics and Applications 2/3 (September2019), 138-140. https://doi.org/10.32323/ujma.556269.
JAMA Romano DA. Pseudo-Valuations on UP-Algebras. Univ. J. Math. Appl. 2019;2:138–140.
MLA Romano, Daniel A. “Pseudo-Valuations on UP-Algebras”. Universal Journal of Mathematics and Applications, vol. 2, no. 3, 2019, pp. 138-40, doi:10.32323/ujma.556269.
Vancouver Romano DA. Pseudo-Valuations on UP-Algebras. Univ. J. Math. Appl. 2019;2(3):138-40.

Cited By

Pseudo-UP ideals and pseudo-UP filters in pseudo-UP algebras
Mathematical Sciences and Applications E-Notes
Daniel A. ROMANO
https://doi.org/10.36753/mathenot.630110

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Universal Journal of Mathematics and Applications 

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