Branchwise solid generalized <em>BCH</em>-algebras

Muhammad Anwar Chaudhry; Asfand Fahad; Yongsheng Rao; Muhammad Imran Qureshi; Salma Gulzar; Muhammad Anwar Chaudhry; Asfand Fahad; Yongsheng Rao; Muhammad Imran Qureshi; Salma Gulzar

doi:10.3934/math.2020160

AIMS Mathematics

2020, Volume 5, Issue 3: 2424-2432. doi: 10.3934/math.2020160

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Research article

Branchwise solid generalized BCH-algebras

1.
Department of Mathematics and Statistics, Institute of Southern Punjab, Multan 66000, Pakistan
2.
Department of Mathematics, COMSATS University Islamabad (Vehari Campus),Vehari 61100, Pakistan
3.
Institute of Computing Science and Technology, Guangzhou University, Guangzhou 510006, China

Received: 27 October 2019 Accepted: 25 February 2020 Published: 05 March 2020
MSC : Primary: 06F35, 03G25; Secondary: 03G25

In this paper, we investigate an equivalent condition for a branchwise strongly solid gBCH-algebra to be branchwise commutative. Moreover, we show that a branchwise strongly solid gBCH-algebra is both branchwise commutative and branchwise positive implicative if and only if it is branchwise implicative.
Citation: Muhammad Anwar Chaudhry, Asfand Fahad, Yongsheng Rao, Muhammad Imran Qureshi, Salma Gulzar. Branchwise solid generalized BCH-algebras[J]. AIMS Mathematics, 2020, 5(3): 2424-2432. doi: 10.3934/math.2020160

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Abstract

In this paper, we investigate an equivalent condition for a branchwise strongly solid gBCH-algebra to be branchwise commutative. Moreover, we show that a branchwise strongly solid gBCH-algebra is both branchwise commutative and branchwise positive implicative if and only if it is branchwise implicative.

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