Embedding modes into semimodules, part III

• Autorzy: Pilitowska A. , Romanowska A. B.
• Języki publikacji: EN

Abstrakty

EN

In the first part of this paper, we considered the problem of constructing a (commutative unital) semiring defining the variety of semimodules whose idempotent subreducts lie in a given variety of modes. We provided a general construction of such semirings, along with basic examples and some general properties. In the second part of the paper we discussed some selected varieties of modes, in particular, varieties of affine spaces, varieties of barycentric algebras and varieties of semilattice modes, and described the semirings determining their semi-linearizations, the varieties of semimodules having these algebras as idempotent subreducts. The third part is devoted to varieties of differential groupoids and more general differential modes, and provides the semirings of the semi-linearizations of these varieties.

Słowa kluczowe

EN

modes (idempotent entropic algebras); idempotent reducts and subreducts of (semi)modules over commutative (semi)rings; differential groupoids; differential modes

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2011
• Tom: Vol. 44, nr 4
• Strony: 791--800
• Opis fizyczny: Bibliogr. 10 poz.

Twórcy

autor

Pilitowska A.

autor

Romanowska A. B.

• Faculty Of Mathematics And Information Science Warsaw University Of Technology Pl. Politechniki 1 00-661 Warsaw, Poland,

Bibliografia

• [1] U. Hebisch, H. J.Weinert, Semirings - Algebraic Theory and Application in Computer Science, World Scientific, Singapore, 1998.
• [2] K. A. Kearnes, Semilattice modes I: the associated semiring, Algebra Universalis 34 (1995), 220–272.
• [3] A. Kravchenko, A. Pilitowska, A. Romanowska, D. Stanovský, Differential modes, Internat. J. Algebra Comput. 18(3) (2008), 567–588.
• [4] A. Pilitowska, A. Romanowska, Embedding modes into semimodules, Part I, Demonstratio Math. 44 (2011), 523–534.
• [5] A. Pilitowska, A. Romanowska, Embedding modes into semimodules, Part II, Demonstratio Math., this volume, 781–790.
• [6] A. Pilitowska, A. Romanowska, D. Stanovský, Varieties of differential modes embeddable into semimodules, Internat. J. Algebra Comput. 19 (2009), 669–680.
• [7] A. B. Romanowska, Semi-affine modes and modals, Sci. Math. Jpn. 61 (2005), 159–194.
• [8] A. B. Romanowska, J. D. H. Smith, Modal Theory, Heldermann Verlag, Berlin, 1985.
• [9] A. B. Romanowska, J. D. H. Smith, Differential groupoids, Contributions to General Algebra 7 (1991), 283–290.
• [10] A. B. Romanowska, J. D. H. Smith, Modes, World Scientific, Singapore, 2002.