Tbilisi Mathematical Journal

On the second radical elements of lattice modules

Narayan Phadatare and Vilas Kharat

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text

Abstract

Let $L$ be a $C$-lattice and $M$ be a lattice module over $L$. For a non-zero element $N\in M$, join of all second elements $X$ of $M$ with $X\leq N$ is called the second radical of $N$, and it is denoted by $\sqrt[s]{N}$. In this paper, we study some properties of second radical of elements of $M$ and obtain some related results.

Article information

Source
Tbilisi Math. J., Volume 11, Issue 4 (2018), 165-173.

Dates
Received: 9 November 2017
Accepted: 10 November 2018
First available in Project Euclid: 4 January 2019

Permanent link to this document
https://projecteuclid.org/euclid.tbilisi/1546570892

Digital Object Identifier
doi:10.32513/tbilisi/1546570892

Mathematical Reviews number (MathSciNet)
MR3954214

Subjects
Primary: 06B23: Complete lattices, completions
Secondary: 06B75: Generalizations of lattices

Keywords
minimal element second element second radical element

Citation

Phadatare, Narayan; Kharat, Vilas. On the second radical elements of lattice modules. Tbilisi Math. J. 11 (2018), no. 4, 165--173. doi:10.32513/tbilisi/1546570892. https://projecteuclid.org/euclid.tbilisi/1546570892


Export citation

References

  • H. Ansari-Toroghy and F. Farshadifar On the dual notion of prime radicals of submodules, Asian-Eur. J. Math., 6(2)(2013) 1350024(11 pages). doi: 10.1142/S1793557113500241.
  • E. A. AL-Khouja, Maximal elements and prime elements in lattice modules, Damascus Univ. Basic Sci., 19(2003), 9-20.
  • A. Francisco, D. D. Anderson and C. Jayaram, Some results on abstract commutative ideal theory, Period. Math. Hungar., 30(1)(1995), 1-26.
  • S. Ballal and V. Kharat, Zariski topology on lattice modules, Asian-Eur. J. Math., 8(2015), 1550066(10 pages). doi: 10.1142/S1793557115500667.
  • S. Ballal and V. Kharat, On $\phi$-absorbing primary elements in lattice modules, Algebra, (2015), 183930(6 pages). doi: 10.1155/ 2015/183930.
  • F. Callialp and U. Tekir, Multiplication lattice modules, Iran. J. Sci. Technol., A4(2011), 309-313.
  • F. Callialp, U. Tekir and E. Aslan Karayigit, On multiplication lattice modules, Hacet. J. Math. Stat., 43(4) (2014), 571-579.
  • F. Callialp, U. Tekir and G. Ulucak, Comultiplication lattice modules, Iran. J. Sci. Technol., 39(A2) (2015), 213-220.
  • J. A. Johnson, a-adic completions of Noetherian lattice modules, Fund. Math., 66(1970), 341-371.
  • N. Phadatare, S. Ballal and V. Kharat, On the second spectrum of lattice modules, Discuss. Math. Gen. Algebra Appl, 37(2017), 59-74. doi:10.7151/dmgaa.1266.
  • N. Phadatare, S. Ballal and V. Kharat, Semi-complement graph of lattice modules, Soft Computing. doi: 10.1007/s00500-018-3347-y.
  • N. K. Thakare, C. S. Manjarekar and S. Maeda, Abstract spectral theory-II: minimal characters and minimal spectrums of multiplicative lattices, Acta Sci. Math. 52(1988), 53-67.
  • N. K. Thakare and C. S. Manjarekar, Abstract spectral theory: Multiplicative lattices in which every character is contained in a unique maximal character, Lecture Notes in Pure and Appl.Math., 91(1984), Dekker(New York).
  • S. Yassemi, The dual notion of prime submodules, Arch. Math.(Brno), 37(2001), 273-278.