2026· Far East Journal of Mathematical Sciences (FJMS)· Vol 143, pp. 4207-4217· 0 citations
Abstract
The monoidal product \(\odot\) of an MV-algebra determines an annihilation relation that differs from the classical lattice polar. On order ideals, iteration of the corresponding annihilator twice produces a closure operator. Its fixed points are compared with zero-productabsorbing, ⊙ -semiprime, and ⊙ -prime order ideals. Primality implies both semiprimeness and zero-product absorption, whereas counterexamples account for every remaining pairwise implication that fails. A direct computation in each finite MV-chain \(\mathbf{L}_{n}\) gives the annihilators and the exact conditions for the other three properties.
Consider a free product $(M,\varphi)= (M_1,\varphi_1)* (M_2,\varphi_2)$ of non-trivial von Neumann algebras. Using amalgamated free product techniques, we establish irreducibility and weak spectral gap results for free product subalgebras and the centralizer subalgebra of the free product state. In particular, it is sh...
Aldo Garcia Guinto, Fehmi Ekin Giritlioglu, R. RahulKumar et al.· 0 citations
We construct a family of finite local rings whose annihilating-ideal graphs are naturally described by orthogonality of subspaces of $\mathbb{F}_2^n$. For $n=4$ we determine the clique and chromatic numbers exactly and obtain \[ \omega(\AG(R_4))=5<6=\chi(\AG(R_4)). \] Thus $\AG(R_4)$ is not weakly perfect, and the Behb...
Generalizing the setting of the second author's work on indecomposable modules without nonzero hollow factors, we characterize quivers $Q$ for which the dual algebra $R$ of the path coalgebra of $Q$, equivalently the complete path algebra, has no nonzero uniform right ideals: this happens exactly when every vertex of $...
Let $K/\mathbb{Q}_p$ be a finite extension, and let $X/K$ be an algebraic variety. We present a new proof that the unipotent completion of the \'etale fundamental group of $X_{\bar{K}}$ is a pro-de Rham representation, and show that it is pro-semi-stable whenever $X$ has semi-stable \'etale cohomology. We also reprove,...
We investigate and characterize order automorphisms on the set of partial isometries in the finite-dimensional matrix algebra $M_n(\mathbb{C})$. Different from the classical order automorphisms of subspace lattices, which can be implemented by standard invertible or unitary transformations, the order automorphisms cons...
Let $\mathcal M$ be a diffuse semifinite von Neumann algebra endowed with a faithful normal semifinite trace $\tau$. We prove that, for every nonzero Banach space $Y$, the projective tensor product $L_1(\mathcal M,\tau)\widehat{\otimes}_{\pi}Y$ has the operator Daugavet property. Moreover, the witnessing operators may...
Jun-Xiang Qi, Qi Liu, Yong-Jin Li· 0 citations
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