Let $A$ be a Banach algebra and $X$ be a Banach $A$-bimodule. Then ${mathcal{S}}=A oplus X$, the $l^1$-direct sum of $A$ and $X$ becomes a module extension Banach algebra when equipped with the algebra product $(a,x).(a',x')=(aa',ax'+xa').$ In this paper, we investigate biflatness and biprojectivity for these Banach algebras. We also discuss on automatic continuity of derivations on ${mathcal{S...

This paper attempts to generalize universal algebras on classical sets to $L$-sets when $L$ is a GL-quantale. Some basic notions of fuzzy universal algebra on an $L$-set are introduced, such as subalgebra, quotient algebra, homomorphism, congruence, and direct product etc. The properties of them are studied. $L$-valued power algebra is also introduced and it is shown there is an onto homomorphi...

Many ninth grade students are required to take Algebra I, and extra support is needed for underprepared students. A common solution is to double the amount of mathematics instruction but educators do not agree on how to use the extra time. One common intervention is to enroll these students in a year long Algebra I course, where they are taught Algebra during these double class periods. We comp...

we consider a 2-dimensional representation of the hecke algebra h(g7; u), whereg7 is the complex re ection group and u is the set of indeterminatesu = (x1; x2; y1; y2; y3; z1; z2; z3):after specializing the indetrminates to non zero complex numbers, we then determine a nec-essary and sucient condition that guarantees the irreducibility of the complex specializationof the representation of the ...

‎let $pa$ be a commutative banach algebra and $ex$ be a left banach $pa$-module‎. ‎we study the set‎ ‎$dec_{pa}(ex)$ of all elements in $pa$ which induce a decomposable multiplication operator on $ex$‎. ‎in the case $ex=pa$‎, ‎$dec_{pa}(pa)$ is the well-known apostol algebra of $pa$‎. ‎we show that $dec_{pa}(ex)$ is intimately related with the largest spectrally separable subalgebra of $pa$ and...

abstract. in this paper, we introduce the notion of fuzzy obstinate ideals in mv -algebras. some properties of fuzzy obstinate ideals are given. not only we give some characterizations of fuzzy obstinate ideals, but also bring the extension theorem of fuzzy obstinate ideal of an mv -algebra a. we investigate the relationships between fuzzy obstinate ideals and the other fuzzy ideals of an mv -a...

Most of the research in foundations of mathematics that I do in some way or another involves the use of nonstandard models. I will give a few examples, and indicate what is involved. 1. General algebra and measurable cardinals. An unexpectedly direct connection. 2. Borel selection and higher set theory. A descriptive set theoretic context extensively pursued by some functional analysts. 3. Equa...

We define a family of Dirac operators for the Dunkl angular momentum algebra depending on certain central elements group Pin cover Weyl inherent to rational Cherednik algebra. prove an analogue Vogan's conjecture this and use show that cohomology, when non-zero, determines character representations Furthermore, interpreting in framework (deformed) Howe dualities, we natural element yields, up s...