Characterizations of incidence modules

Naseer Ullah; Hailou Yao; Qianqian Yuan; Muhammad Azam

Czechoslovak Mathematical Journal (2024)

  • Volume: 74, Issue: 4, page 1127-1144
  • ISSN: 0011-4642

Abstract

top
Let R be an associative ring and M be a left R -module. We introduce the concept of the incidence module I ( X , M ) of a locally finite partially ordered set X over M . We study the properties of I ( X , M ) and give the necessary and sufficient conditions for the incidence module to be an IN-module, -module, nil injective module and nonsingular module, respectively. Furthermore, we show that the class of -modules is closed under direct product and upper triangular matrix modules.

How to cite

top

Ullah, Naseer, et al. "Characterizations of incidence modules." Czechoslovak Mathematical Journal 74.4 (2024): 1127-1144. <http://eudml.org/doc/299629>.

@article{Ullah2024,
abstract = {Let $R$ be an associative ring and $M$ be a left $R$-module. We introduce the concept of the incidence module $I(X, M)$ of a locally finite partially ordered set $X$ over $M$. We study the properties of $I(X, M)$ and give the necessary and sufficient conditions for the incidence module to be an IN-module, -module, nil injective module and nonsingular module, respectively. Furthermore, we show that the class of -modules is closed under direct product and upper triangular matrix modules.},
author = {Ullah, Naseer, Yao, Hailou, Yuan, Qianqian, Azam, Muhammad},
journal = {Czechoslovak Mathematical Journal},
keywords = {Ikeda Nakayama module; essential Ikeda Nakayama module; nil injective; nonsingular},
language = {eng},
number = {4},
pages = {1127-1144},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Characterizations of incidence modules},
url = {http://eudml.org/doc/299629},
volume = {74},
year = {2024},
}

TY - JOUR
AU - Ullah, Naseer
AU - Yao, Hailou
AU - Yuan, Qianqian
AU - Azam, Muhammad
TI - Characterizations of incidence modules
JO - Czechoslovak Mathematical Journal
PY - 2024
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 74
IS - 4
SP - 1127
EP - 1144
AB - Let $R$ be an associative ring and $M$ be a left $R$-module. We introduce the concept of the incidence module $I(X, M)$ of a locally finite partially ordered set $X$ over $M$. We study the properties of $I(X, M)$ and give the necessary and sufficient conditions for the incidence module to be an IN-module, -module, nil injective module and nonsingular module, respectively. Furthermore, we show that the class of -modules is closed under direct product and upper triangular matrix modules.
LA - eng
KW - Ikeda Nakayama module; essential Ikeda Nakayama module; nil injective; nonsingular
UR - http://eudml.org/doc/299629
ER -

References

top
  1. Agnarsson, G., Amitsur, S. A., Robson, J. C., 10.1007/BF02785529, Isr. J. Math. 96 (1996), 1-13. (1996) Zbl0878.16015MR1432722DOI10.1007/BF02785529
  2. Ahmed, F. A., Abdul-Jabbar, A. M., 10.1063/5.0104696, AIP Conf. Proc. 2554 (2023), Article ID 020012. (2023) DOI10.1063/5.0104696
  3. Al-Thukair, F., Singh, S., Zaguia, I., 10.1007/s00013-003-4590-7, Arch. Math. 80 (2003), 358-362. (2003) Zbl1044.16025MR1982835DOI10.1007/s00013-003-4590-7
  4. Camillo, V., Nicholson, W. K., Yousif, M. F., 10.1006/jabr.1999.8217, J. Algebra 226 (2000), 1001-1010. (2000) Zbl0958.16002MR1752773DOI10.1006/jabr.1999.8217
  5. Derakhshan, M., Sahebi, S., Javadi, H. H. S., 10.1007/s12215-021-00610-0, Rend. Circ. Mat. Palermo (2) 71 (2022), 145-151. (2022) Zbl1496.16003MR4397978DOI10.1007/s12215-021-00610-0
  6. Doubilet, P., Rota, G.-C., Stanley, R., On the foundations of combinatorial theory. VI. The idea of generating function, Proceedings of the Sixth Berkeley Symposium on Mathematical Statistics and Probability. Volume II. Probability Theory University of California Press, Berkeley (1972), 267-318. (1972) Zbl0267.05002MR0403987
  7. Esin, S., Kanuni, M., Koç, A., 10.1080/00927872.2010.512589, Commun. Algebra 39 (2011), 3836-3848. (2011) Zbl1263.16030MR2845605DOI10.1080/00927872.2010.512589
  8. Ikeda, M., Nakayama, T., 10.1090/S0002-9939-1954-0060489-9, Proc. Am. Math. Soc. 5 (1954), 15-19. (1954) Zbl0055.02602MR0060489DOI10.1090/S0002-9939-1954-0060489-9
  9. Rota, G.-C., 10.1007/BF00531932, Z. Wahrscheinlichkeitstheor. Verw. Geb. 2 (1964), 340-368. (1964) Zbl0121.02406MR0174487DOI10.1007/BF00531932
  10. Spiegel, E., O'Donnell, C. J., Incidence Algebra, Pure and Applied Mathematics, Marcel Dekker 206. Marcel Dekker, New York (1997). (1997) Zbl0871.16001MR1445562
  11. Ssevviiri, D., Groenewald, N., 10.1080/00927872.2012.718822, Commun. Algebra 42 (2014), 571-577. (2014) Zbl1295.16011MR3169589DOI10.1080/00927872.2012.718822
  12. Stanley, R. P., 10.1007/978-1-4615-9763-6, Wadsworth & Brooks/Cole Advanced Books & Software, Monterey (1986). (1986) Zbl0608.05001MR0847717DOI10.1007/978-1-4615-9763-6

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.