In the 19th problem of [1], J. S. Golan put forward the following question: 'For what kind of ring R is it true that the map γ_#:R-tors→S-tors is surjective for every ring surjective homomorphism r: R→S?' w...In the 19th problem of [1], J. S. Golan put forward the following question: 'For what kind of ring R is it true that the map γ_#:R-tors→S-tors is surjective for every ring surjective homomorphism r: R→S?' where both R and S are associative rings with identity, R-tors stands for a lattice composed of all hereditary torsion theories in left R-module category R-Mod and for each τ ∈ R-tors, γ_#(τ)=σ=(f_σ,f_σ)∈S-tors, in展开更多
A partial order on the set of the prime knots can be defined by the existence of a surjective homomorphism between knot groups. In the previous paper, we determined the partial order in the knot table. In this paper, ...A partial order on the set of the prime knots can be defined by the existence of a surjective homomorphism between knot groups. In the previous paper, we determined the partial order in the knot table. In this paper, we prove that 31 and 41 are minimal elements. Further, we study which surjection a pair of a periodic knot and its quotient knot induces, and which surjection a degree one map can induce.展开更多
文摘In the 19th problem of [1], J. S. Golan put forward the following question: 'For what kind of ring R is it true that the map γ_#:R-tors→S-tors is surjective for every ring surjective homomorphism r: R→S?' where both R and S are associative rings with identity, R-tors stands for a lattice composed of all hereditary torsion theories in left R-module category R-Mod and for each τ ∈ R-tors, γ_#(τ)=σ=(f_σ,f_σ)∈S-tors, in
基金Grand-in-Aid for Scientific Research (No.17540064 and No.18840008)
文摘A partial order on the set of the prime knots can be defined by the existence of a surjective homomorphism between knot groups. In the previous paper, we determined the partial order in the knot table. In this paper, we prove that 31 and 41 are minimal elements. Further, we study which surjection a pair of a periodic knot and its quotient knot induces, and which surjection a degree one map can induce.
