Operads for $n$-ary algebras – calculations and conjectures

Martin Markl; Elisabeth Remm

Displaying similar documents to “Operads for $n$ -ary algebras – calculations and conjectures”

Monadic $n \times m$ -valued Łukasiewicz-Moisil algebras

A. V. Figallo, Claudia A. Sanza (2012)

Mathematica Bohemica

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Here we initiate an investigation into the class $m L M_{n \times m}$ of monadic $n \times m$ -valued Łukasiewicz-Moisil algebras (or $m L M_{n \times m}$ -algebras), namely $n \times m$ -valued Łukasiewicz-Moisil algebras endowed with a unary operation. These algebras constitute a generalization of monadic $n$ -valued Łukasiewicz-Moisil algebras. In this article, the congruences on these algebras are determined and subdirectly irreducible algebras are characterized. From this last result it is proved that $m L M_{n \times m}$ is a discriminator variety and as a consequence,...

Mac Neille completion of centers and centers of Mac Neille completions of lattice effect algebras

Martin Kalina (2010)

Kybernetika

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If element $z$ of a lattice effect algebra $(E, \oplus, 0, 1)$ is central, then the interval $[0, z]$ is a lattice effect algebra with the new top element $z$ and with inherited partial binary operation $\oplus$ . It is a known fact that if the set $C (E)$ of central elements of $E$ is an atomic Boolean algebra and the supremum of all atoms of $C (E)$ in $E$ equals to the top element of $E$ , then $E$ is isomorphic to a subdirect product of irreducible effect algebras ([18]). This means that if there exists a MacNeille completion $\hat{E}$ of $E$ which...

Global left loop structures on spheres

Michael K. Kinyon (2000)

Commentationes Mathematicae Universitatis Carolinae

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On the unit sphere $𝕊$ in a real Hilbert space $𝐇$ , we derive a binary operation $⊙$ such that $(𝕊, ⊙)$ is a power-associative Kikkawa left loop with two-sided identity $𝐞_{0}$ , i.e., it has the left inverse, automorphic inverse, and $A_{l}$ properties. The operation $⊙$ is compatible with the symmetric space structure of $𝕊$ . $(𝕊, ⊙)$ is not a loop, and the right translations which fail to be injective are easily characterized. $(𝕊, ⊙)$ satisfies the left power alternative and left Bol identities “almost everywhere” but not...

Hopf algebra structure $H^{σ - R}$ with two sided invertible 2-cocycle

Shuan Hong Wang, Dingguo Wang (1999)

Commentationes Mathematicae Universitatis Carolinae

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In this paper, we study the $H^{σ - R}$ type Hopf algebras and present its braided and quasitriangular Hopf algebra structure. This generalizes well-known results on $H^{σ}$ and $H^{R}$ type Hopf algebras. Finally, the classification of $H^{σ - R}$ type Hopf algebras is given.

Displaying similar documents to “Operads for n -ary algebras – calculations and conjectures”

Monadic n × m -valued Łukasiewicz-Moisil algebras

Mac Neille completion of centers and centers of Mac Neille completions of lattice effect algebras

Global left loop structures on spheres

Hopf algebra structure H σ - R with two sided invertible 2-cocycle

Displaying similar documents to “Operads for $n$ -ary algebras – calculations and conjectures”

Monadic $n \times m$ -valued Łukasiewicz-Moisil algebras

Hopf algebra structure $H^{σ - R}$ with two sided invertible 2-cocycle