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Branimir Seselja: L-E-groups |
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| L-E-Groups (Branimir Seselja, University of Novi Sad) Abstract. A lattice valued E-group, briefly an L-E-group, is a quadruple (G; mu ; E^{mu}; L), where G = (G; . , ^{-1}, e) is an algebra of the type (2,1,0) (not necessarily a group), L is a complete lattice, mu is a function G --> L, E^{mu} is a function G^2-->L. In addition, mu fulfills particular closedness properties, and E^{mu} act as a lattice valued equality satisfying group-like identities - special lattice theoretic formulas. We prove basic features of L-E-groups: properties of fundamental operations, cancellability, solvability of equations, substructure properties and others. As a direct connection to classical groups, we prove that an L-E-group uniquely determines a collection of subalgebras of algebra G, whose quotient structures over the corresponding congruences - cuts of E - are classical groups, and vice versa. |
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| Location : Bolyai Intézet, I. Kórház, fszt. 17., folyóirat-olvasó terem | ||||
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