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On the structure of C-algebras through atomicity and if-then-else

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This paper investigates the notions of atoms and atomicity in C-algebras and obtains a characterisation of atoms in the C-algebra of transformations. In this connection, various characterisations for the existence of suprema of subsets of C-algebras are obtained. Further, this work presents some necessary conditions and some sufficient conditions for the atomicity of C-algebras and shows that the class of finite atomic C-algebras is precisely the class of finite adas. This paper also uses the intrinsic if-then-else action to study the structure of C-algebras and classify the elements of the C-algebra of transformations.

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Acknowledgements

We are thankful to the referee for his/her comments which have improved the presentation and readability of the paper.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, Indian Institute of Technology Kanpur, Kanpur, India

    Gayatri Panicker

  2. Department of Mathematics, Indian Institute of Technology Guwahati, Guwahati, India

    K. V. Krishna

  3. Department of Computer Science and Engineering, Indian Institute of Technology Guwahati, Guwahati, India

    Purandar Bhaduri

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  1. Gayatri Panicker
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  2. K. V. Krishna
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  3. Purandar Bhaduri
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Correspondence to K. V. Krishna.

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Presented by Tim Stokes.

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Panicker, G., Krishna, K.V. & Bhaduri, P. On the structure of C-algebras through atomicity and if-then-else. Algebra Univers. 81, 22 (2020). https://doi.org/10.1007/s00012-020-0648-7

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