ترغب بنشر مسار تعليمي؟ اضغط هنا

Avoidable Sets in The Bicyclic Inverse Semigroup

141   0   0.0 ( 0 )
 نشر من قبل Nandor Sieben
 تاريخ النشر 2007
  مجال البحث
والبحث باللغة English
 تأليف Nandor Sieben




اسأل ChatGPT حول البحث

A subset $U$ of a set $S$ with a binary operation is called {it avoidable} if $S$ can be partitioned into two subsets $A$ and $B$ such that no element of $U$ can be written as a product of two distinct elements of $A$ or as the product of two distinct elements of $B$. The avoidable sets of the bicyclic inverse semigroup are classified.

قيم البحث

اقرأ أيضاً

We study algebraic and topological properties of topological semigroups containing a copy of the bicyclic semigroup C(p,q). We prove that each topological semigroup S with pseudocompact square contains no dense copy of C(p,q). On the other hand, we c onstruct a (consistent) example of a pseudocompact (countably compact) Tychonov semigroup containing a copy of C(p,q).
In this paper, we study product-free subsets of the free semigroup over a finite alphabet $A$. We prove that the maximum density of a product-free subset of the free semigroup over $A$, with respect to the natural measure that assigns a weight of $|A |^{-n}$ to each word of length $n$, is precisely $1/2$.
We define the notion of $D$-set in an arbitrary semigroup, and with some mild restrictions we establish its dynamical and combinatorial characterizations. Assuming a weak form of cancellation in semigroups we have shown that the Cartesian product of finitely many $D$-sets is a $D$-set. A similar partial result has been proved for Cartesian product of infinitely many $D$-sets. Finally, in a commutative semigroup we deduce that $D$-sets (with respect to a F{o}lner net) are $C$-sets.
109 - Xiuwen Yang , Ligong Wang 2020
The concept of energy of a signed digraph is extended to iota energy of a signed digraph. The energy of a signed digraph $S$ is defined by $E(S)=sum_{k=1}^n|text{Re}(z_k)|$, where $text{Re}(z_k)$ is the real part of eigenvalue $z_k$ and $z_k$ is the eigenvalue of the adjacency matrix of $S$ with $n$ vertices, $k=1,2,ldots,n$. Then the iota energy of $S$ is defined by $E(S)=sum_{k=1}^n|text{Im}(z_k)|$, where $text{Im}(z_k)$ is the imaginary part of eigenvalue $z_k$. In this paper, we consider a special graph class for bicyclic signed digraphs $mathcal{S}_n$ with $n$ vertices which have two vertex-disjoint signed directed even cycles. We give two iota energy orderings of bicyclic signed digraphs, one is including two positive or two negative directed even cycles, the other is including one positive and one negative directed even cycles.
The structure of the automorphism group of the sandwich semigroup IS_n is described in terms of standard group constructions.
التعليقات
جاري جلب التعليقات جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
mircosoft-partner

هل ترغب بارسال اشعارات عن اخر التحديثات في شمرا-اكاديميا