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  • We present a complete description of subdirectly irreducible state BL-algebras as well as of subdirectly irreducible state-morphism BL-algebras. In addition, we present a general theory of state-morphism algebras, that is, algebras of general type with state-morphism which is a fixed idempotent endomorphism. We define a diagonal state-morphism algebra and we show that every subdirectly irreducible state-morphism algebra can be embedded into a diagonal one. We describe generators of the varieties of state-morphism algebras, in particular generators of state-morphism BL-algebras, state-morphism MTL-algebras, state-morphism non-associative BL-algebras, and state-morphism pseudo MV-algebras.
  • We present a complete description of subdirectly irreducible state BL-algebras as well as of subdirectly irreducible state-morphism BL-algebras. In addition, we present a general theory of state-morphism algebras, that is, algebras of general type with state-morphism which is a fixed idempotent endomorphism. We define a diagonal state-morphism algebra and we show that every subdirectly irreducible state-morphism algebra can be embedded into a diagonal one. We describe generators of the varieties of state-morphism algebras, in particular generators of state-morphism BL-algebras, state-morphism MTL-algebras, state-morphism non-associative BL-algebras, and state-morphism pseudo MV-algebras. (en)
Title
  • State-morphism algebras - General approach
  • State-morphism algebras - General approach (en)
skos:prefLabel
  • State-morphism algebras - General approach
  • State-morphism algebras - General approach (en)
skos:notation
  • RIV/61989592:15310/13:33146291!RIV14-MSM-15310___
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  • O
http://linked.open...iv/cisloPeriodika
  • 1 May 2013
http://linked.open...vai/riv/dodaniDat
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  • 107712
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  • RIV/61989592:15310/13:33146291
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  • Pseudo MV-algebra; Non-associative BL-algebra; MTL-algebra; Non-associative t-norm; t-Norm; Diagonal subalgebra; Generator; Congruence extension property; State-morphism algebra; State BL-algebra; State MV-algebra (en)
http://linked.open.../riv/klicoveSlovo
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  • NL - Nizozemsko
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  • [2632819ADE46]
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  • Fuzzy Sets and Systems
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  • 218
http://linked.open...iv/tvurceVysledku
  • Botur, Michal
  • Dvurečenskij, Anatolij
http://linked.open...ain/vavai/riv/wos
  • 000317160700006
issn
  • 0165-0114
number of pages
http://bibframe.org/vocab/doi
  • 10.1016/j.fss.2012.08.013
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  • 15310
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