Let A be a unital, commutative and finitely generated ring. We prove that if n ≥ 4, then the group G = ELn(A) has a fixed point property for affine isometric actions on B. Here B stands for any L space or any Banach space isomorphic to a Hilbert space. We also verify that the comparison map Ψ : H b (G,B) → H(G,B) from bounded to ordinary cohomology is injective, where G and B are as in above. F...

For any reductive Lie algebra g and commutative, associative, unital algebra S, we give a complete classification of the simple weight modules of g ⊗ S with finite weight multiplicities. In particular, any such module is parabolically induced from a simple admissible module for a Levi subalgebra. Conversely, all modules obtained in this way have finite weight multiplicities. These modules are i...

This is the first in a series of papers highlighting applications reduced and coreduced modules. Let $R$ be commutative unital ring $I$ an ideal $R$. We show that $I$-reduced $R$-modules $I$-coreduced provide setting which Matlis-Greenless-May (MGM) Equivalence Greenless-May (GM) Duality hold. These two notions have been hitherto only known to exist derived category setting. realise $I$-torsion...

In this paper, we generalize the Mandelbrot set using quaternions and spherical coordinates. particular, use pure to define a product. This product, which is inspired by product of complex numbers, add angles multiply radii We show that algebraic structure with commutative unital magma. Then, present several generalizations set. Among them, visually identical so-called Mandelbulb. bounded it ca...

we show that the character space of the vector-valued lipschitz algebra $lip^{alpha}(x, e)$ of order $alpha$ is homeomorphic to the cartesian product $xtimes m_e$ in the product topology, where $x$ is a compact metric space and $e$ is a unital commutative banach algebra. we also characterize the form of each character on $lip^{alpha}(x, e)$. by appealing to the injective tensor product, we then...

The reticulation L(R) of a commutative ring R was introduced by Joyal in 1975, then the theory developed Simmons remarkable paper published 1980. is bounded distributive algebra whose main property that Zariski prime spectrum Spec(R) and Stone SpecId (L(R)) are homeomorphic. construction lattice generalized Belluce for each unital defined axioms. In recent we algebras semidegenerate congruence-...

We provide a generalization of Mundici's equivalence between unital Abelian lattice-ordered groups and MV-algebras: the category commutative is equivalent to MV-monoidal algebras. Roughly speaking, structures we call are without unary operation $x \mapsto -x$. The primitive operations $+$, $\lor$, $\land$, $0$, $1$, $-1$. A prime example these $\mathbb{R}$, with obvious interpretation operation...

Let $L$ be an integral and commutative quantale. In this paper, by fuzzifying the notion of generalized neighborhood systems, the notion of $L$-fuzzy generalized neighborhoodsystem is introduced and then a pair of lower and upperapproximation operators based on it are defined and discussed. It is proved that these approximation operators include generalized neighborhood system...