On Lattice Vector Spaces over a Distributive Lattice

Pallavi Panjarike; Kuncham Syam Prasad; Madeline Al-Tahan; Vadiraja Bhatta; Harikrishnan Panackal

doi:10.1007/978-981-99-6349-2_10

On Lattice Vector Spaces over a Distributive Lattice

Pallavi Panjarike, Kuncham Syam Prasad, Madeline Al-Tahan, Vadiraja Bhatta, Harikrishnan Panackal^*

^*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Abstract

In this paper, we show a homomorphism between lattices that induces a lattice vector space over a distributive lattice. The notion of congruence relation on lattice vector space is introduced to study the quotient spaces. We obtain a corre-spondence between the set of matrices over distributive lattices and the set of linear transformations.

Original language	English
Title of host publication	Semigroups, Algebras and Operator Theory - ICSAOT 2022
Editors	A.A. Ambily, V.B. Kiran Kumar
Publisher	Springer
Pages	173-183
Number of pages	11
ISBN (Print)	9789819963485
DOIs	https://doi.org/10.1007/978-981-99-6349-2_10
Publication status	Published - 01-02-2024
Event	International Conference on Semigroup, Algebras, and Operator Theory, ICSAOT 2022 - Cochin, India Duration: 28-03-2022 → 31-03-2022

Publication series

Name	Springer Proceedings in Mathematics and Statistics
Volume	436
ISSN (Print)	2194-1009
ISSN (Electronic)	2194-1017

Conference

Conference	International Conference on Semigroup, Algebras, and Operator Theory, ICSAOT 2022
Country/Territory	India
City	Cochin
Period	28-03-22 → 31-03-22

All Science Journal Classification (ASJC) codes

General Mathematics

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10.1007/978-981-99-6349-2_10

Cite this

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title = "On Lattice Vector Spaces over a Distributive Lattice",

abstract = "In this paper, we show a homomorphism between lattices that induces a lattice vector space over a distributive lattice. The notion of congruence relation on lattice vector space is introduced to study the quotient spaces. We obtain a corre-spondence between the set of matrices over distributive lattices and the set of linear transformations.",

author = "Pallavi Panjarike and {Syam Prasad}, Kuncham and Madeline Al-Tahan and Vadiraja Bhatta and Harikrishnan Panackal",

note = "Publisher Copyright: {\textcopyright} The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023.; International Conference on Semigroup, Algebras, and Operator Theory, ICSAOT 2022 ; Conference date: 28-03-2022 Through 31-03-2022",

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Panjarike, P, Syam Prasad, K, Al-Tahan, M, Bhatta, V & Panackal, H 2024, On Lattice Vector Spaces over a Distributive Lattice. in AA Ambily & VB Kiran Kumar (eds), Semigroups, Algebras and Operator Theory - ICSAOT 2022. Springer Proceedings in Mathematics and Statistics, vol. 436, Springer, pp. 173-183, International Conference on Semigroup, Algebras, and Operator Theory, ICSAOT 2022, Cochin, India, 28-03-22. https://doi.org/10.1007/978-981-99-6349-2_10

On Lattice Vector Spaces over a Distributive Lattice. / Panjarike, Pallavi; Syam Prasad, Kuncham; Al-Tahan, Madeline et al.
Semigroups, Algebras and Operator Theory - ICSAOT 2022. ed. / A.A. Ambily; V.B. Kiran Kumar. Springer, 2024. p. 173-183 (Springer Proceedings in Mathematics and Statistics; Vol. 436).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

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AB - In this paper, we show a homomorphism between lattices that induces a lattice vector space over a distributive lattice. The notion of congruence relation on lattice vector space is introduced to study the quotient spaces. We obtain a corre-spondence between the set of matrices over distributive lattices and the set of linear transformations.

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On Lattice Vector Spaces over a Distributive Lattice

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