Geodesic
On minimal spectrum of multiplication lattice modules
Mathematica Bohemica, Tome 144 (2019) no. 1, pp. 85-97
Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

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 $M$.
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 $M$.
DOI : 10.21136/MB.2018.0094-17
Classification : 06D10, 06E10, 06E99, 06F99
Keywords: prime element; mimimal prime element; Zariski topology 
@article{10_21136_MB_2018_0094_17,
     author = {Ballal, Sachin and Kharat, Vilas},
     title = {On minimal spectrum of multiplication lattice modules},
     journal = {Mathematica Bohemica},
     pages = {85--97},
     year = {2019},
     volume = {144},
     number = {1},
     doi = {10.21136/MB.2018.0094-17},
     mrnumber = {3934199},
     zbl = {07088837},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.21136/MB.2018.0094-17/}
}
TY  - JOUR
AU  - Ballal, Sachin
AU  - Kharat, Vilas
TI  - On minimal spectrum of multiplication lattice modules
JO  - Mathematica Bohemica
PY  - 2019
SP  - 85
EP  - 97
VL  - 144
IS  - 1
UR  - http://geodesic.mathdoc.fr/articles/10.21136/MB.2018.0094-17/
DO  - 10.21136/MB.2018.0094-17
LA  - en
ID  - 10_21136_MB_2018_0094_17
ER  - 
%0 Journal Article
%A Ballal, Sachin
%A Kharat, Vilas
%T On minimal spectrum of multiplication lattice modules
%J Mathematica Bohemica
%D 2019
%P 85-97
%V 144
%N 1
%U http://geodesic.mathdoc.fr/articles/10.21136/MB.2018.0094-17/
%R 10.21136/MB.2018.0094-17
%G en
%F 10_21136_MB_2018_0094_17
Ballal, Sachin; Kharat, Vilas. On minimal spectrum of multiplication lattice modules. Mathematica Bohemica, Tome 144 (2019) no. 1, pp. 85-97. doi: 10.21136/MB.2018.0094-17

[1] Alarcon, F., Anderson, D. D., Jayaram, C.: Some results on abstract commutative ideal theory. Period. Math. Hung. 30 (1995), 1-26. | DOI | MR | JFM

[2] Al-Khouja, E. A.: Maximal elements and prime elements in lattice modules. Damascus University Journal for Basic Sciences 19 (2003), 9-21.

[3] Ballal, S., Kharat, V.: Zariski topology on lattice modules. Asian-Eur. J. Math. 8 (2015), Article ID 1550066, 10 pages. | DOI | MR | JFM

[4] Calliap, F., Tekir, U.: Multiplication lattice modules. Iran. J. Sci. Technol., Trans. A, Sci. 35 (2011), 309-313. | DOI | MR | JFM

[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). | MR

[6] Dilworth, R. P.: Abstract commutative ideal theory. Pac. J. Math. 12 (1962), 481-498. | DOI | MR | JFM

[7] Keimel, K.: A unified theory of minimal prime ideals. Acta Math. Acad. Sci. Hung. 23 (1972), 51-69. | DOI | MR | JFM

[8] Manjarekar, C. S., Kandale, U. N.: Baer elements in lattice modules. Eur. J. Pure Appl. Math. 8 (2015), 332-342. | MR | JFM

[9] Pawar, Y. S., Thakare, N. K.: The space of minimal prime ideals in a 0-distributive semilattice. Period. Math. Hung. 13 (1982), 309-319. | DOI | MR | JFM

[10] Phadatare, N., Ballal, S., Kharat, V.: On the second spectrum of lattice modules. Discuss. Math. Gen. Algebra Appl. 37 (2017), 59-74. | DOI | MR

[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. | MR | JFM

[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. | MR | JFM

Cité par Sources :