This paper studies two homogenizations of the down-up algebras introduced in [1]. We show that in all cases the homogenizing variable is not a zero-divisor, and that when the parameter β is non-zero, the homogenized down-up algebra is a Noetherian domain and a maximal order, and also Artin-Schelter regular, Auslander regular, and Cohen-Macaulay. We show that all homogenized down-up algebras hav...

In this paper we investigate some hereditary properties of amenability modulo an ideal of Banach algebras. We show that if $(e_alpha)_alpha$ is a bounded approximate identity modulo I of a Banach algebra A and X is a neo-unital modulo I, then $(e_alpha)_alpha$ is a bounded approximate identity for X. Moreover we show that amenability modulo an ideal of a Banach algebra A can be only considered ...

Let $mathfrak{L}$ be the Virasoro-like algebra and $mathfrak{g}$ itsderived algebra, respectively. We investigate the structure of the Lie triplederivation algebra of $mathfrak{L}$ and $mathfrak{g}$. We provethat they are both isomorphic to $mathfrak{L}$, which provides twoexamples of invariance under triple derivation.

in this paper we investigate some hereditary properties of amenability modulo an ideal of banach algebras. we show that if (e) is a bounded approximate identity modulo i of a banach algebra a and x is a neo-unital modulo i, then (e) is a bounded approximate identity for x. moreover we show that amenability modulo an ideal of a banach algebra a can be only considered by the neo-unital modulo...

Ladkin and Maddux [LaMa87] showed how to interpret the calculus of time intervals defined by Allen [AZ2831 in terms of representations of a particular relation algebra, and proved that this algebra has a unique countable representation up to isomorphism. In this paper, we . consider the algebra An of n-intervals, which coincides with Allen’s algebra for n=2, and prove that An has a unique count...

In this paper, we study pseudo-valuations on a BCI-algebra and obtain some related results. The relation between pseudo-valuations and ideals is investigated. We use a pseudo-metric induced by a pseudovaluation to introduce a congruence relation on a BCI-algebra. We define the quotient algebra induced by this relation and prove that it is also a BCI-algebra and study its properties.

this paper provides a review on major ergodic features of semi-independent hyper mv {algebra dynamical systems. theorems are presentedto make contribution to calculate the entropy. particularly, it is proved that thetotal entropy of those semi-independent hyper mv {algebra dynamical systemsthat have a generator can be calculated with respect to their generator ratherthan considering all the par...

in this article, we introduce monomial irreducible representations of the special linear lie algebra $sln$. we will show that this kind of representations have bases for which the action of the chevalley generators of the lie algebra on the basis elements can be given by a simple formula.

– We prove that any multi-filtered algebra with semi-commutative associated graded algebra can be endowed with a locally finite filtration keeping up the semi-commutativity of the associated graded algebra. As consequences, we obtain that Gelfand–Kirillov dimension is exact for finitely generated modules and that the algebra is finitely partitive. Our methods apply to algebras of current intere...