On generalized derivations of partially ordered sets

Ahmed Y. Abdelwanis; Abdelkarim Boua

Communications in Mathematics (2019)

  • Volume: 27, Issue: 1, page 69-78
  • ISSN: 1804-1388

Abstract

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Let P be a poset and d be a derivation on P . In this research, the notion of generalized d -derivation on partially ordered sets is presented and studied. Several characterization theorems on generalized d -derivations are introduced. The properties of the fixed points based on the generalized d -derivations are examined. The properties of ideals and operations related with generalized d -derivations are studied.

How to cite

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Abdelwanis, Ahmed Y., and Boua, Abdelkarim. "On generalized derivations of partially ordered sets." Communications in Mathematics 27.1 (2019): 69-78. <http://eudml.org/doc/294363>.

@article{Abdelwanis2019,
abstract = {Let $P$ be a poset and $d$ be a derivation on $P$. In this research, the notion of generalized $d$-derivation on partially ordered sets is presented and studied. Several characterization theorems on generalized $d$-derivations are introduced. The properties of the fixed points based on the generalized $d$-derivations are examined. The properties of ideals and operations related with generalized $d$-derivations are studied.},
author = {Abdelwanis, Ahmed Y., Boua, Abdelkarim},
journal = {Communications in Mathematics},
keywords = {Generalized $d$-derivation; fixed point; ideal; partially ordered set},
language = {eng},
number = {1},
pages = {69-78},
publisher = {University of Ostrava},
title = {On generalized derivations of partially ordered sets},
url = {http://eudml.org/doc/294363},
volume = {27},
year = {2019},
}

TY - JOUR
AU - Abdelwanis, Ahmed Y.
AU - Boua, Abdelkarim
TI - On generalized derivations of partially ordered sets
JO - Communications in Mathematics
PY - 2019
PB - University of Ostrava
VL - 27
IS - 1
SP - 69
EP - 78
AB - Let $P$ be a poset and $d$ be a derivation on $P$. In this research, the notion of generalized $d$-derivation on partially ordered sets is presented and studied. Several characterization theorems on generalized $d$-derivations are introduced. The properties of the fixed points based on the generalized $d$-derivations are examined. The properties of ideals and operations related with generalized $d$-derivations are studied.
LA - eng
KW - Generalized $d$-derivation; fixed point; ideal; partially ordered set
UR - http://eudml.org/doc/294363
ER -

References

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  1. Alshehri, N. O., Generalized derivations of lattices, Int. J. Contemp. Math. Sciences, 5, 13, 2010, 629-640, (2010) MR2668457
  2. Ceven, Y., Ozturk, M. A., 10.4134/BKMS.2008.45.4.701, Bull. Korean Math. Soc., 45, 4, 2008, 701-707, (2008) MR2463146DOI10.4134/BKMS.2008.45.4.701
  3. Chajda, I., Rachůnek, J., 10.1007/BF00353659, Order, 5, 1989, 407-423, (1989) MR1010389DOI10.1007/BF00353659
  4. Gierz, G., Hofmann, K.H., Keimel, K., Lawson, J.D., Mislove, M., Scott, D.S., Continuous Lattices and Domains, 2003, Cambridge University Press, (2003) Zbl1088.06001MR1975381
  5. Gölbasi, Ö., Notes on prime near-rings with generalized derivation, Southeast Asian Bull. Math., 30, 2006, 49-54, (2006) MR2213799
  6. Hvala, B., 10.1080/00927879808826190, Comm. Alg., 26, 1998, 1147-1166, (1998) Zbl0899.16018MR1612208DOI10.1080/00927879808826190
  7. Larmerová, J., Rachůnek, J., Translations of distributive and modular ordered sets, Acta Univ. Palack. Olomuc. Fac. Rerum Natur. Math., 27, 1988, 13-23, (1988) MR1039879
  8. Ozturk, M. A., Yazarli, H., Kim, K. H., 10.2989/QM.2009.32.3.10.911, Quaest. Math., 32, 3, 2009, 415-425, (2009) MR2569104DOI10.2989/QM.2009.32.3.10.911
  9. Rachůnek, J., Translations des ensembles ordonnés, Math. Slovaca., 31, 1981, 337-340, (1981) MR0637961
  10. Szasz, G., Derivations of lattices, Acta Sci. Math. (Szeged), 37, 1975, 149-154, (1975) MR0382090
  11. Ullah, Z., Javaid, I., Chaudhary, M.A., On generalized tripel derivations on lattices, Ars Combinatoria, 113, 2014, 463-471, (2014) MR3186490
  12. Xin, X.L., Li, T.Y., Lu, J.H., 10.1016/j.ins.2007.08.018, Inform. Sci., 178, 2008, 307-316, (2008) MR2363221DOI10.1016/j.ins.2007.08.018
  13. Zhang, H., Li, Q., On derivations of partially ordered sets, Math. Slovaca, 67, 1, 2017, 17-22, (2017) MR3630149

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