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See detailReconstructing multisets over commutative groupoids and affine functions over nonassociative semirings
Lehtonen, Erkko UL

in International Journal of Algebra and Computation (2014), 24(1), 11-31

A reconstruction problem is formulated for multisets over commutative groupoids. The cards of a multiset are obtained by replacing a pair of its elements by their sum. Necessary and sufficient conditions ... [more ▼]

A reconstruction problem is formulated for multisets over commutative groupoids. The cards of a multiset are obtained by replacing a pair of its elements by their sum. Necessary and sufficient conditions for the reconstructibility of multisets are determined. These results find an application in a different kind of reconstruction problem for functions of several arguments and identification minors: classes of linear or affine functions over nonassociative semirings are shown to be weakly reconstructible. Moreover, affine functions of sufficiently large arity over finite fields are reconstructible. [less ▲]

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See detailAdditive decomposability of functions over abelian groups
Couceiro, Miguel UL; Lehtonen, Erkko UL; Waldhauser, Tamás UL

in International Journal of Algebra and Computation (2013), 23(3), 643-662

Abelian groups are classified by the existence of certain additive decompositions of group-valued functions of several variables.

Detailed reference viewed: 174 (4 UL)