Tbilisi Mathematical Journal

On the second radical elements of lattice modules

Narayan Phadatare and Vilas Kharat

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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

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

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

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

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

minimal element second element second radical element


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

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