Bijections between $τ$-rigid modules
We describe a special bijection between the indecomposable summands of two basic $τ$-tilting modules.
math.RT↗
arXiv subjects
H. Melis Tekin Akcin
Publications and source records attributed to H. Melis Tekin Akcin.
A bijection between the indecomposable summands of two multiplicity free tilting modules
We show that there is a reflection type bijection between the indecomposable summands of two multiplicity free tilting modules $X$ and $Y$. This bijection fixes the common indecomposable summands of $X$ and $Y$ and sends indecomposable projective (resp., injective) summands of exactly one module to non-projective (resp., non-injective) summands of the other. Moreover, this bijection interchanges the two possible non-isomorphic complements of an almost complete tilting module.
math.RT↗
An analogue of Amitsur's property for the ring of pseudo-differential operators
Let R be a ring with a derivation δ. In this paper, we prove that an analogue of Amitsur's property holds for left T-nilpotent radideals of pseudo-differential operator rings R((x^{-1}; δ)), where R is a delta-compatible ring. As a direct consequence of this fact, we obtain an alternative characterization of the prime radical of R((x^{-1}; δ)).
math.RA↗
On symmetric property of skew polynomial rings
Symmetric rings were introduced by Lambek to extend usual commutative ideal theory in noncommutative rings. In this paper, we study symmetric rings over which Ore extensions are symmetric. A ring R is called strongly σ-symmetric if the skew polynomial ring R[x;σ] is symmetric. We consider some properties and extensions of strongly σ-symmetric rings. Then we show the relationship between strongly σ-symmetric rings and other classes of rings. We next argue the polynomial extensions over strongly σ-symmetric rings. Moreover, we prove that if R is a σ-rigid ring, then R[x]/(x_n) is a strongly σ-symmetric ring, where σis an endomorphism of R, (x_n) is the ideal generated by x_n and n is a positive integer; and that if the classical left quotient ring Q(R) of R exists, then R is σ-symmetric if and only if Q(R) is strongly σ-symmetric.
math.RA↗