On minimal spectrum of multiplication lattice modules

Sachin Ballal; Vilas Kharat

Mathematica Bohemica (2019)

  • Volume: 144, Issue: 1, page 85-97
  • ISSN: 0862-7959

Abstract

top
We study the minimal prime elements of multiplication lattice module M over a C -lattice L . Moreover, we topologize the spectrum π ( M ) of minimal prime elements of M and study several properties of it. The compactness of π ( M ) is characterized in several ways. Also, we investigate the interplay between the topological properties of π ( M ) and algebraic properties of M .

How to cite

top

Ballal, Sachin, and Kharat, Vilas. "On minimal spectrum of multiplication lattice modules." Mathematica Bohemica 144.1 (2019): 85-97. <http://eudml.org/doc/294554>.

@article{Ballal2019,
abstract = {We study the minimal prime elements of multiplication lattice module $M$ over a $C$-lattice $L$. Moreover, we topologize the spectrum $\pi (M)$ of minimal prime elements of $M$ and study several properties of it. The compactness of $\pi (M)$ is characterized in several ways. Also, we investigate the interplay between the topological properties of $\pi (M)$ and algebraic properties of $M$.},
author = {Ballal, Sachin, Kharat, Vilas},
journal = {Mathematica Bohemica},
keywords = {prime element; mimimal prime element; Zariski topology},
language = {eng},
number = {1},
pages = {85-97},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On minimal spectrum of multiplication lattice modules},
url = {http://eudml.org/doc/294554},
volume = {144},
year = {2019},
}

TY - JOUR
AU - Ballal, Sachin
AU - Kharat, Vilas
TI - On minimal spectrum of multiplication lattice modules
JO - Mathematica Bohemica
PY - 2019
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 144
IS - 1
SP - 85
EP - 97
AB - We study the minimal prime elements of multiplication lattice module $M$ over a $C$-lattice $L$. Moreover, we topologize the spectrum $\pi (M)$ of minimal prime elements of $M$ and study several properties of it. The compactness of $\pi (M)$ is characterized in several ways. Also, we investigate the interplay between the topological properties of $\pi (M)$ and algebraic properties of $M$.
LA - eng
KW - prime element; mimimal prime element; Zariski topology
UR - http://eudml.org/doc/294554
ER -

References

top
  1. Alarcon, F., Anderson, D. D., Jayaram, C., 10.1007/BF01876923, Period. Math. Hung. 30 (1995), 1-26. (1995) Zbl0822.06015MR1318850DOI10.1007/BF01876923
  2. Al-Khouja, E. A., Maximal elements and prime elements in lattice modules, Damascus University Journal for Basic Sciences 19 (2003), 9-21. (2003) 
  3. Ballal, S., Kharat, V., 10.1142/S1793557115500667, Asian-Eur. J. Math. 8 (2015), Article ID 1550066, 10 pages. (2015) Zbl1342.06011MR3424141DOI10.1142/S1793557115500667
  4. Calliap, F., Tekir, U., 10.22099/ijsts.2011.2156, Iran. J. Sci. Technol., Trans. A, Sci. 35 (2011), 309-313. (2011) Zbl1315.06017MR2958883DOI10.22099/ijsts.2011.2156
  5. Culhan, D. S., Associated Primes and Primal Decomposition in Modules and Lattice Modules, and Their Duals, Thesis (Ph.D.), University of California, Riverside (2005). (2005) MR2707457
  6. Dilworth, R. P., 10.2140/pjm.1962.12.481, Pac. J. Math. 12 (1962), 481-498. (1962) Zbl0111.04104MR0143781DOI10.2140/pjm.1962.12.481
  7. Keimel, K., 10.1007/BF01889903, Acta Math. Acad. Sci. Hung. 23 (1972), 51-69. (1972) Zbl0265.06016MR0318037DOI10.1007/BF01889903
  8. Manjarekar, C. S., Kandale, U. N., Baer elements in lattice modules, Eur. J. Pure Appl. Math. 8 (2015), 332-342. (2015) Zbl06698174MR3373893
  9. Pawar, Y. S., Thakare, N. K., 10.1007/BF01849242, Period. Math. Hung. 13 (1982), 309-319. (1982) Zbl0532.06004MR0698578DOI10.1007/BF01849242
  10. Phadatare, N., Ballal, S., Kharat, V., 10.7151/dmgaa.1266, Discuss. Math. Gen. Algebra Appl. 37 (2017), 59-74. (2017) MR3648183DOI10.7151/dmgaa.1266
  11. Thakare, N. K., Manjarekar, C. S., Abstract spectral theory: Multiplicative lattices in which every character is contained in a unique maximal character, Algebra and Its Applications. Int. Symp. Algebra and Its Applications, 1981, New Delhi, India Lect. Notes Pure Appl. Math. 91. Marcel Dekker Inc., New York (1984), 265-276 H. L. Manocha et al. (1984) Zbl0551.06012MR0750867
  12. Thakare, N. K., Manjarekar, C. S., Maeda, S., Abstract spectral theory. II: Minimal characters and minimal spectrums of multiplicative lattices, Acta Sci. Math. 52 (1988), 53-67. (1988) Zbl0653.06002MR0957788

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.