Relative (pre-)anti-flexible algebrasnand associated algebraic structures

Algebraic Structures

Algebraic Structures

In this text, we focus on operations of arity 2, 1, and 0. – For n = 2, f : A → A is a binary operation and is usually written in infix notation, using a binary operation symbol like ·, ∗, or +. Hence, instead of f(a1, a2) we write a1fa2. – For n = 1, f : A→ A is a unary operation. – For n = 0, f : A → A is a nullary operation or a constant. An algebra (or an algebraic structure) is a set A, th...

MAGMA-JOINED-MAGMAS: A CLASS OF NEW ALGEBRAIC STRUCTURES

By left magma-$e$-magma, I mean a set containingthe fixed element $e$, and equipped by two binary operations "$cdot$", $odot$ with the property $eodot (xcdot y)=eodot(xodot y)$, namelyleft $e$-join law. So, $(X,cdot,e,odot)$ is a left magma-$e$-magmaif and only if $(X,cdot)$, $(X,odot)$ are magmas (groupoids), $ein X$ and the left $e$-join law holds.Right (and two-sided) magma-$e$-magmas are de...

Algebraic Structures on Hyperkähler Manifolds Algebraic Structures on Hyperkähler Manifolds

Let M be a compact hyperkähler manifold. The hy-perkähler structure equips M with a set R of complex structures parametrized by CP 1 , called the set of induced complex structures. It was known previously that induced complex structures are non-algebraic, except may be a countable set. We prove that a countable set of induced complex structures is algebraic, and this set is dense in R. A more g...

Algebraic structures of soft sets associated with new operations

Recently new operations have been defined for soft sets. In this paper, we study some important properties associated with these new operations. A collection of all soft sets with respect to new operations give rise to four idempotent monoids. Then with the help of these monoids we can study semiring (hemiring) structures of soft sets. Some of these semirings (hemirings) are actually lattices. ...