Other language title :
ﯾﺎدداﺷﺖ ﮐﻮﺗﺎﻫﯽ در ﻣﻮرد رﺳﺘﻪﻫﺎي ﻣﻌﺎدل از ﺷﺒﻪ EMV-ﺟﺒﺮﻫﺎي ﺳﺮه ﺿﻌﯿﻒ
Title of article :
A short note on categorical equivalences of proper weak pseudo EMV-algebras
Author/Authors :
Dvurečenskij, A 1Mathematical Institute - Slovak Academy of Sciences, Slovakia
Abstract :
We study the class of weak pseudo EMV-algebras without top element that are a non-commutative generalization of MValgebras,
pseudo MV-algebras and generalized Boolean algebras. We present their categorical equivalences to a special
category of pseudo MV-algebras with a fixed maximal and normal ideal as well as to a special category of unital ℓ-groups with
a fixed maximal and normal ℓ-ideal.
Farsi abstract :
ﭼﮑﯿﺪه . در اﯾﻦ ﻣﻘﺎﻟﻪ، ﺷﺒﻪ EMV-ﺟﺒﺮﻫﺎي ﺿﻌﯿﻒ، ﺑﺪون ﺑﺰرﮔﺘﺮﯾﻦ ﻋﻀﻮ، را ﻣﻄﺎﻟﻌﻪ ﻣﯽﮐﻨﯿﻢ ﮐﻪ ﺗﻌﻤﯿﻢ ﻏﯿﺮﺟﺎﺑﻪﺟﺎﯾﯽ از MV-ﺟﺒﺮﻫﺎ، ﺷﺒﻪ MV-ﺟﺒﺮﻫﺎ و ﺟﺒﺮ ﺑﻮﻟﯽ ﺗﻌﻤﯿﻢ ﯾﺎﻓﺘﻪ اﺳﺖ. ﺳﭙﺲ رﺳﺘﻪﻫﺎي آن را ﮐﻪ ﺑﺎ -l ﺟﺒﺮﻫﺎ ﺑﺎ ﯾﮏ اﯾﺪهآل ﻣﺎﮐﺴﯿﻤﺎل و ﻧﺮﻣﺎل ﺛﺎﺑﺖ و ﻫﻤﭽﻨﯿﻦ رﺳﺘﻪ ﺧﺎﺻﯽ از-MV ﯾﮏ رﺳﺘﻪ ﺧﺎﺻﯽ از ﺷﺒﻪ ﮔﺮوهﻫﺎي واﺣﺪ ﺑﺎ ﯾﮏ l-اﯾﺪه آل ﻣﺎﮐﺴﯿﻤﺎل و ﻧﺮﻣﺎل ﺛﺎﺑﺖ ﻣﻌﺎدل ﻫﺴﺘﻨﺪ، را اراﺋﻪ ﻣﯽﮐﻨﯿﻢ.
Keywords :
Weak pseudo EMV-algebra , pseudo MV-algebra , idempotent element , representation of wPEMV-algebras , proper wPEMV-algebra , associated wPEMV-algebra , categorial equivalence , unital l-group
Journal title :
Journal of Algebraic Hyperstructures and Logical Algebras
