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A ring R is called NLI (rings whose nilpotent elements form a Lie ideal) if for each aN(R) and bR, abbaN(R). Clearly, NI rings are NLI. In this note, many properties of NLI rings are studied. The main results we obtain are the following: (1) NLI rings are directly finite and left min-abel; (2) If R is a NLI ring, then (a) R is a strongly regular ring if and only if R is a Von Neumann regular ring; (b) R is (weakly) exchange if and only if R is (weakly) clean; (c) R is a reduced ring if and only if R is a n-regular ring; (3) If R is a NLI left MC2 ring whose singular simple left modules are Wnil-injective, then R is reduced.

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A recently published paper [6] considered the total graph of commutative ring R. In this paper, we compute Wiener, hyper-Wiener, reverse Wiener, Randić, Zagreb, ABC and GA indices of zero-divisor graph.

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The classification of Bruce and Gaffney respectively Gibson and Hobbs for simple plane curve singularities respectively simple space curve singularities is characterized in terms of invariants. This is the basis for the implementation of a classifier in the computer algebra system singular.

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The maximal Orlicz spaces such that the mixed logarithmic means of multiple Walsh-Fourier series for the functions from these spaces converge in measure and in norm are found.

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Let V be the 2-dimensional column vector space over a finite field
\documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$\mathbb{F}_q$$ \end{document}
(where q is necessarily a power of a prime number) and let ℙq be the projective line over
\documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$\mathbb{F}_q$$ \end{document}
. In this paper, it is shown that GL 2(q), for q ≠ 3, and SL 2(q) acting on V − {0} have the strict EKR property and GL 2(3) has the EKR property, but it does not have the strict EKR property. Also, we show that GL n(q) acting on
\documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$\left( {\mathbb{F}_q } \right)^n - \left\{ 0 \right\}$$ \end{document}
has the EKR property and the derangement graph of PSL 2(q) acting on ℙq, where q ≡ −1 (mod 4), has a clique of size q + 1.
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We study basic properties of the generalized ideal transforms D I (M, N) and the set of associated primes of the modules R i D I (M, N).

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Let G be a finite group. A subgroup H of G is called an
\documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$\mathcal{H}$$ \end{document}
-subgroup in G if N G(H) ∩ H gH for all gG. A subgroup H of G is called a weakly
\documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$\mathcal{H}$$ \end{document}
-subgroup in G if there exists a normal subgroup K of G such that G = HK and HK is an
\documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$\mathcal{H}$$ \end{document}
-subgroup in G. In this article, we investigate the structure of a group G in which every subgroup with order p m of a Sylow p-subgroup P of G is a weakly
\documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$\mathcal{H}$$ \end{document}
-subgroup in G, where m is a fixed positive integer. Our results improve and extend the main results of Skiba [13], Jaraden and Skiba [11], Guo and Wei [8], Tong-Veit [15] and Li et al. [12].
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A new generalization of the logarithmic series distribution has been obtained as a limiting case of the zero-truncated Mishra’s [10] generalized negative binomial distribution (GNBD). This distribution has an advantage over the Mishra’s [9] quasi logarithmic series distribution (QLSD) as its moments appear in compact forms unlike the QLSD. This makes the estimation of parameters easier by the method of moments. The first four moments of this distribution have been obtained and the distribution has been fitted to some well known data-sets to test its goodness of fit.

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An upper bound is given on the size of a k-fan-free 3-graph, and an infinite family reaching this bound is also described.

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Applying certain convexity arguments we investigate the existence of a classical solution for a Dirichlet problem for which the Euler action functional is not necessarily differentiable in the sense of Gâteaux.

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