Communications of the Korean Mathematical Society (대한수학회논문집)

Korean Mathematical Society (대한수학회)
권호 표지
DOI QR코드

DOI QR Code

CLASSIFYING MONOIDS BY QUASI-ANNIHILATOR (HOMO)FLATNESS OF THEIR RIGHT REES FACTORS

  • Aminizadeh, Reza (Department of Mathematics Science and Research Branch Islamic Azad University) ;
  • Rasouli, Hamid (Department of Mathematics Science and Research Branch Islamic Azad University) ;
  • Tehranian, Abolfazl (Department of Mathematics Science and Research Branch Islamic Azad University)
  • Received : 2019.09.09
  • Accepted : 2020.01.21
  • Published : 2020.07.31
Download PDF
⟨ Previous Next ⟩

Abstract

In this paper, the class of quasi-annihilator (homo)flat acts based on the notion of quasi-annihilator ideal is introduced. This class lies strictly between the classes of weakly (homo)flat and principally weakly (homo)flat acts. Some properties of such kinds of flatness are studied. We present some homological classifications for monoids by means of quasiannihilator (homo)flatness of their right Rees factor acts.

Keywords

References

  1. S. Bulman-Fleming, The classification of monoids by flatness properties of acts, in Semigroups and applications (St. Andrews, 1997), 18-38, World Sci. Publ., River Edge, NJ, 1998.
  2. S. Bulman-Fleming, Absolutely annihilator-flat monoids, Semigroup Forum 65 (2002), no. 3, 428-449. https://doi.org/10.1007/s002330010136
  3. S. Bulman-Fleming and M. Kilp, Equalizers and flatness properties of acts, Comm. Algebra 30 (2002), no. 3, 1475-1498. https://doi.org/10.1081/AGB-120004883
  4. M. Kilp, On flat acts, Tartu Ul. Toimetised 253 (1970), 66-72 (in Russian).
  5. M. Kilp, Classification of monoids by the properties of their Rees factor-polygons, Tartu Riikl. Ul. Toimetised 640 (1983), 29-37.
  6. M. Kilp, U. Knauer, and A. V. Mikhalev, Monoids, Acts and Categories, De Gruyter Expositions in Mathematics, 29, Walter de Gruyter & Co., Berlin, 2000. https://doi.org/10.1515/9783110812909
  7. V. Laan, Pullbacks and flatness properties of acts, Dissertationes Mathematicae Universitatis Tartuensis, 15, Tartu University Press, Tartu, 1999.
  8. V. Laan, When torsion free acts are principally weakly flat, Semigroup Forum 60 (2000), no. 2, 321-325. https://doi.org/10.1007/s002339910024
  9. V. Laan, Pullbacks and flatness properties of acts. I, Comm. Algebra 29 (2001), no. 2, 829-850. https://doi.org/10.1081/AGB-100001547
  10. V. Laan, Pullbacks and flatness properties of acts. II, Comm. Algebra 29 (2001), no. 2, 851-878. https://doi.org/10.1081/AGB-100001548
  11. X. Liang and Y. Luo, On a generalization of condition (PW P), Bull. Iranian Math. Soc. 42 (2016), no. 5, 1057-1076.
  12. P. Normak, On equalizer-flat and pullback-flat acts, Semigroup Forum 36 (1987), no. 3, 293-313. https://doi.org/10.1007/BF02575023
  13. H. Qiao and W. Liu, The weakly pullback flat properties of right Rees factor S-acts, Pure Math. Appl. (PU.M.A.) 18 (2007), no. 3-4, 311-318.
  14. H. Rashidi, A. Golchin, and H. Mohammadzadeh Saany, On GPW-flat acts, Categories and General Algebraic Structures with Applications 12 (2020), no. 1, 25-42. https://doi.org/10.29252/CGASA.12.1.25
  15. J. Renshaw, Flatness and amalgamation in monoids, J. London Math. Soc. (2) 33 (1986), no. 1, 73-88. https://doi.org/10.1112/jlms/s2-33.1.73
  16. J. Renshaw, Monoids for which condition (P) acts are projective, Semigroup Forum 61 (2000), no. 1, 45-56. https://doi.org/10.1007/PL00006014
  17. M. Sedaghatjoo, V. Laan, and M. Ershad, Principal weak flatness and regularity of diagonal acts, Comm. Algebra 40 (2012), no. 11, 4019-4030. https://doi.org/10.1080/00927872.2011.600747
  18. B. Stenstrom, Flatness and localization over monoids, Math. Nachr. 48 (1971), 315-334. https://doi.org/10.1002/mana.19710480124