In this paper, by using the Nörlund mean Nt and the notion of ideal double convergence, we introduce new sequence spaces c0Ι2 (Nt), and ℓ∞I2 (Nt). Besides, we study some topological and algebraic properties on these spaces. Furthermore, some inclusion concerning these spaces are proved.
In this article, the notions of $ I_{2} $-localized and $ I_{2}^{*} $-localized sequences in metric spaces are defined. Besides, we study some properties associated to $ I_{2} $-localized and $ I_{2} $-Cauchy sequences. On the other hand, we define the notion of uniformly $ I_{2} $-localized sequences in metric spaces.
The second cohomology group (SCG) of the Jordan superalgebra [Formula: see text], [Formula: see text], over an algebraically closed field [Formula: see text] of characteristic zero is calculated by using the coefficients which appear in the regular superbimodule Reg [Formula: see text]. Contrary to the case of algebras, this group is nontrivial thanks to the non-splitting caused by the Wedderburn Decomposition Theorem [F. A. Gómez-González, Wedderburn principal theorem for Jordan superalgebras I, J. Algebra 505 (2018) 1–32]. First, to calculate the SCG of a Jordan superalgebra we use split-null extension of the Jordan superalgebra and the Jordan superalgebra representation. We prove conditions that satisfy the bilinear forms [Formula: see text] that determine the SCG in Jordan superalgebras. We use these to calculate the SCG for the Jordan superalgebra [Formula: see text], [Formula: see text]. Finally, we prove that [Formula: see text], [Formula: see text].
We investigate an analogue to the Wedderburn Principal Theorem (WPT) for a finite-dimensional Jordan superalgebra J with solvable radical N such that N 2 = 0 and J/N ∼ = JPn, n ≥ 3.We consider N as an irreducible JPn-bimodule and we prove that the WPT holds for J.
We consider a finite-dimensional Jordan superalgebra $$\mathcal {A}$$
A
over a field of characteristic zero $$\mathbb {F}$$
F
such that $$\mathcal {N}$$
N
is the solvable radical of $$\mathcal {A}$$
A
. We proved that if $$\mathcal {N}\,^2=0$$
N
2
=
0
and $$\mathcal {A}/\mathcal {N}$$
A
/
N
is isomorphic to simple Jordan superalgebra of Grassmann Poisson bracket $$\mathfrak {K}\textrm{an}(2)$$
K
an
(
2
)
, then an analogous to Wedderburn Principal Theorem (WPT) holds.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.