DOI QR코드

DOI QR Code

WEAKLY PRIME LEFT IDEALS IN NEAR-SUBTRACTION SEMIGROUPS

  • 발행 : 2008.07.31

초록

In this paper we introduce the notion of weakly prime left ideals in near-subtraction semigroups. Equivalent conditions for a left ideal to be weakly prime are obtained. We have also shown that if (M, L) is a weak $m^*$-system and if P is a left ideal which is maximal with respect to containing L and not meeting M, then P is weakly prime.

키워드

참고문헌

  1. J. C. Abbott, Sets, Lattices and Boolean Algebras, Allyn and Bacon, Boston, 1969
  2. P. Dheena and G. Satheesh Kumar, On strongly regular near-subtraction semigroups, Commun. Korean Math. Soc. 22 (2007), no. 3, 323-330 https://doi.org/10.4134/CKMS.2007.22.3.323
  3. Y. B. Jun, H. S. Kim, and E. H. Roh, Ideal theory of subtraction algebras, Scientiae Mathematicae Japonicae 61 (2005), no. 3, 459-464
  4. K. H. Kim, On Subtraction Semigroups, Scientiae Mathematicae Japonicae 62 (2005), no. 2, 273-280
  5. K. H. Kim, E. H. Roh, and Y. H. Yon, A note on a subtraction semigroup, Scientiae Mathematicae Japonicae, 60 (2004), no. 3, 451-459
  6. E. H. Roh, K. H. Kim, and J. G. Lee, On Prime and Semiprime ideals in Subtraction Semigroups, Scientiae Mathematicae Japonicae, 61 (2005), no. 2, 259-266
  7. B. M. Schein, Difference Semigroups, Communications in algebra 20 (1992), 2153-2169 https://doi.org/10.1080/00927879208824453
  8. B. Zelinka, Subtraction Semigroups, Math. Bohemica 120 (1995), 445-447