Let D be a division ring with involution ⋆ and S the set of all symmetric elements of D. Assume that the center F of D is uncountable and K is a division subring of D containing F. The main aim of this note is to show that S is right algebraic over K if and only if so is D. This result allows us to construct an example of division rings K ⊂ D such that D is right algebraic but not left algebraic over K.
We show that the action of the Kauffman bracket skein algebra of a surface Σ on the skein module of the handlebody bounded by Σ is faithful if and only if the quantum parameter is not a root of 1.
We study finite groups whose rational-valued irreducible characters are all of odd degrees. We conjecture that in such groups, all rational elements must be 2-elements.
A concept of Cohen–Macaulay in codimension t is defined and characterized for arbitrary finitely generated modules and coherent sheaves by Miller, Novik, and Swartz in 2011. Soon after, Haghighi, Yassemi, and Zaare-Nahandi defined and studied CMt simplicial complexes, which is the pure version of the abovementioned concept and naturally generalizes both Cohen–Macaulay and Buchsbaum properties. The purpose of this paper is to survey briefly recent results of CMt simplicial complexes.
We study a class of nonlinear elliptic problems with Dirichlet conditions in the framework of the Sobolev anisotropic spaces with variable exponent, involving an anisotropic operator on an unbounded domain ({varOmega }subset mathbb {R}^{N} (N geq 2)). We prove the existence of entropy solutions avoiding sign condition and coercivity on the lower order terms.
Let f be a transcendental meromorphic function on (mathbb {C},) k be a positive integer, and (Q_{0},Q_{1},dots ,Q_{k}) be polynomials in (mathbb {C}[z]). In this paper, we will prove that the frequency of distinct poles of f is governed by the frequency of zeros of the differential polynomial form (Q_{0}(f)Q_{1}(f^{prime }){dots } Q_{k}(f^{(k)})) in f. We will also prove that the Nevanlinna defect of the differential polynomial form (Q_{0}(f)Q_{1}(f^{prime }){dots } Q_{k}(f^{(k)})) in f satisfies
with suitable conditions on k and the degree of the polynomials. Thus, our work is a generalization of Mues’s conjecture and Goldberg’s conjecture for the more general differential polynomials.
In this paper, we compare annihilators of Tor and Ext modules of finitely generated modules over a commutative noetherian ring. For local Cohen–Macaulay rings, one of our results refines a theorem of Dao and Takahashi.
In this paper, we present necessary and sufficient conditions for existence and uniqueness of solutions of general variational inequalities (GVIs). A Tikhonov-type regularization method to find a solution of GVIs is proposed. Finally, under suitable conditions, we prove that the well-posedness of a GVI is equivalent to the solution existence and uniqueness. The obtained results are compared with the previous ones. In particular, our results generalize corresponding ones for inverse variational inequalities.
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