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SMARANDACHE WEAK BE-ALGEBRAS

Arsham Borumand Saeid
대한수학회 (The Korean Mathematical Society)|2012.07|대한수학회논문집 (Communications of the KMS)|제27권 제3호|pp. 489-496

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참고문헌

키워드

CI-algebrasBE-algebraSmarandache weak BE-algebra(Q-Smarandache) filter(Q-Smarandache) ideal.
주제분류수학

초록

In this paper, we introduce the notions of Smarandache weak $BE$-algebra, $Q$-Smarandache filters and $Q$-Smarandache ideals. We show that a nonempty subset $F$ of a $BE$-algebra $X$ is a $Q$-Smarandache filter if and only if $A(x,y)\subseteq F$, which $A(x,y)$ is a $Q$-Smarandache upper set. The relationship between these notions are stated and proved.

Abstract

In this paper, we introduce the notions of Smarandache weak $BE$-algebra, $Q$-Smarandache filters and $Q$-Smarandache ideals. We show that a nonempty subset $F$ of a $BE$-algebra $X$ is a $Q$-Smarandache filter if and only if $A(x,y)\subseteq F$, which $A(x,y)$ is a $Q$-Smarandache upper set. The relationship between these notions are stated and proved.

참고문헌 (10)

  1. Sun Shin Ahn, "On generalized upper sets in BE-algebras", 대한수학회보, 46(2), pp.281~287 (2009), 대한수학회
  2. S. S. Ahn, "On ideals and upper sets in BE-algebras", Sci. Math. Jpn, 68(2), pp.279~285 (2008)
  3. A. Borumand Saeid, "Smarandache BL-algebra", J. Appl. Log, 8, pp.235~261 (2010)
  4. A. Borumand Saeid, "Smarandache BCH-algebra", World Applied Sci- ences Journal, 7, pp.77~83 (2009)
  5. "Smarandache gropoids"[URL]
  6. H. S. Kim, "On BE-algebras", Sci. Math. Jpn. Online e-2006, pp.1299~1302 (2006)
  7. H. K. Kyung, "A Note on CI-algebras", Int. Math. Forum, 6(1), pp.1~5 (2011)
  8. B. L. Meng, "CI-algebra", Sci. Math. Jpn. Online e-2009, pp.695~701 (2009)
  9. R. Padilla, "Smarandache algebraic structures", Bull. Pure Appl. Sci. Sect. E Math. Stat, 17(1), pp.119~121 (1998)
  10. A. Rezaei, "Some results in BE-algebras, Analele Universitatii Oradea Fasc", Matematica, pp.33~44 (2012)

관련 논문AI추천

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