Related papers: On a Pair of Universal Weak Inverse Property Loops
We suggest that a weak isotriplet composite scalar possessing an unbroken U(1) global symmetry naturally arises in technicolor models leading to an interesting type of dark matter candidate: the iTIMP. We propose explicit models of the…
For an inverse semigroup S with the set of idempotents E and a minimal idempotent, we find necessary and sufficient conditions for the Fourier algebra A(S) to be module amenable, module character amenable, module (operator) biflat, or…
Given a weak distributive law between algebras underlying two weak bialgebras, we present sufficient conditions under which the corresponding weak wreath product algebra becomes a weak bialgebra with respect to the tensor product coalgebra…
Necessary and sufficient conditions are given for a $G$-graded simple module over a unital associative algebra, graded by an abelian group $G$, to be isomorphic to a loop module of a simple module, as well as for two such loop modules to be…
By studying the holomorphic structure of automorphic inverse property quasigroups and loops[AIPQ and (AIPL)] and cross inverse property quasigroups and loops[CIPQ and (CIPL)], it is established that the holomorph of a loop is a Smarandache;…
A new class of rings, {\em the class of weakly left localizable rings}, is introduced. A ring $R$ is called {\em weakly left localizable} if each non-nilpotent element of $R$ is invertible in some left localization $S^{-1}R$ of the ring…
Given two two-dimensional conformal field theories, a domain wall -- or defect line -- between them is called invertible if there is another defect with which it fuses to the identity defect. A defect is called topological if it is…
In this paper, we define and study a particular case of von Neumann regular notion called a weak von Neumann regular ring. It shown that the polynomial ring $R[x]$ is weak von Neumann regular if and only if $R$ has exactly two idempotent…
We prove that any twisted generalized Weyl algebra satisfying certain consistency conditions can be embedded into a crossed product. We also introduce a new family of twisted generalized Weyl algebras, called multiparameter twisted Weyl…
For an infinite discrete group $G$ acting on a compact metric space $X$, we introduce several weak versions of equicontinuity along subsets of $G$ and show that if a minimal system $(X,G)$ admits an invariant measure then $(X,G)$ is distal…
In this paper, we introduce a weak group inverse (called the WG inverse in the present paper) for square matrices of an arbitrary index, and give some of its characterizations and properties. Furthermore, we introduce two orders: one is a…
The Isbell, compact-open and point-open topologies on the set $C(X,\mathbb{R})$ of continuous real-valued maps can be represented as the dual topologies with respect to some collections $\alpha(X)$ of compact families of open subsets of a…
A sign pattern is an array with entries in $\{+,-,0\}$. A matrix $Q$ is row orthogonal if $QQ^T = I$. The Strong Inner Product Property (SIPP), introduced in [B.A.~Curtis and B.L.~Shader, Sign patterns of orthogonal matrices and the strong…
In \cite{Craig}, we introduced a syntactically defined and highly general class of calculi known as \emph{semi-analytic}. We then demonstrated that any sufficiently strong (modal) substructural logic with a semi-analytic calculus must…
The Modular Isomorphism Problem asks if an isomorphism of group algebras of two finite p-groups G and H over a field of characteristic p, implies an isomorhism of the groups G and H. We survey the history of the problem, explain strategies…
We introduce a new type of equivalence between blocks of finite group algebras called a strong isotypy. A strong isotypy is equivalent to a $p$-permutation equivalence and restricts to an isotypy in the sense of Brou\'{e}. To prove these…
The article addresses some open questions about the relations between the topological weak mixing property and the transitivity of the map $f\times f^2 \times...\times f^m$, where $f\colon X\ra X$ is a topological dynamical system on a…
A convergence theorem for martingales with c\`adl\`ag trajectories (right continuous with left limits everywhere) is obtained in the sense of the weak dual topology on Hilbert space, under conditions that are much weaker than those required…
Let G be a reductive group over an algebraically closed field whose characteristic is not a bad prime for G. Let w be an elliptic element of the Weyl group which has minimal length in its conjugacy class. We show that there exists a unique…
For a measure preserving automorphism $T$ of a probability space, we provide conditions on the tail function of $g\colon\Omega\to\mathbb R$ and $g-g\circ T$ which guarantee limit theorems among the weak invariance principle,…