Volume 9, Issue 3 (12-2023)
mmr 2023, 9(3): 178-213 |
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Karimi Shahmarvandi A, Rasouli S, Khaksar Haghani F. Generalize state coannihilators in state residuated lattices. mmr 2023; 9 (3) :178-213
URL: http://mmr.khu.ac.ir/article-1-3210-en.html
URL: http://mmr.khu.ac.ir/article-1-3210-en.html
1- Islamic Azad University, Shahrekord Branch
2- Islamic Azad University, Shahrekord Branch&Persian Gulf University, Bushehr, Iran
3- Islamic Azad University, Shahrekord Branch ,haghani1351@yahoo.com
2- Islamic Azad University, Shahrekord Branch&Persian Gulf University, Bushehr, Iran
3- Islamic Azad University, Shahrekord Branch ,
Abstract: (650 Views)
In this paper we introduce the notion of generalized state coannihilators in state residuated lattices. We establish a connection between generalized state coannihilators and Galois connection. If A is a state residuated lattice, we show that the set of filters forms a Heyting algebra in which the relative pseudo-complement of G with respect to F is (F : G)ν. Also, we show that the set of state coannihilator filters form a Boolean lattice. Ultimately, we characterize generalized state coannihilators in terms of state prime filters and state minimal prime filters.
Keywords: generalized state co annihilators, state residuated lattice, state prime filters, state minimal prime filters.
Type of Study: Original Manuscript |
Subject:
Universal algebra
Received: 2021/07/7 | Revised: 2024/02/21 | Accepted: 2022/04/24 | Published: 2024/01/8 | ePublished: 2024/01/8
Received: 2021/07/7 | Revised: 2024/02/21 | Accepted: 2022/04/24 | Published: 2024/01/8 | ePublished: 2024/01/8
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