Generalized uniserial rings

The following conditions are shown to be equivalent: 1) ring A is generalized uniserial (not necessarily artinian); 2) every finitely presented A module is semiserial; 3) A is semiperfect and the projective cover of every indecomposable finitely presented module is indecomposable.     

Polymorphic transformations and thermal deformations of monoclinic n-paraffins C30H62 and C32H66

Thermal deformations and polymorphic transformations of even long chain monoclinic normal paraffins C₃₀H₆₂ and C₃₂H₆₆ (homological purity 97–99%) are studied. Thermal deformations and temperature limits of the existence of crystalline (1M _cryst and 2M _cryst ), low-temperature rotationally crystalline triclinic (Tc _rot.1), monoclinic (M _rot.1), and orthorhombic (Or _rot.1) and high-temperature rotationally crystalline hexagonal (H _rot.2) phases of these n-paraffins are estimated by the character of changes in their diffraction patterns and unit cell parameters (thermal X-ray diffraction). The molecular structure and conformational composition of these n-paraffins in different phase states are determined (IR spectroscopy). In order to determine the temperatures of phase transitions differential scanning calorimetry is also applied. The data of all three methods are in good agreement with each other. The initial sample of C₃₀H₆₂ n-paraffin at room temperature is characterized by a two-layer monoclinic 2M crystalline modification. When the melt is rapidly cooled, it crystallizes in monolayer monoclinic 1M and orthorhombic Or modifications (two-phase mixture 1M+Or). The initial sample of C₃₂H₆₆ n-paraffin at room temperature is characterized by the monolayer monoclinic modification 1M. When the melt is rapidly cooled, as well as C₃₀H₆₂ n-paraffin, it crystallizes in monolayer monoclinic 1M and orthorhombic Or modifications (two-phase mixture 1M+Or). It is found that both n-paraffin undergo irreversible polymorphic transformations from the crystalline state cryst to the low-temperature rotationally crystalline state rot.1. For C₃₀H₆₂ n-paraffin the transition is performed by the scheme 2M _cryst → M _rot.1 → Or _rot.1, and for C₃₂H₆₆ n-paraffin it is performed by the scheme 1M _cryst → Tc _rot.1. Both paraffins do not undergo the transition to the high-temperature rotationally crystalline state rot.2 (hexagonal phase H _rot.2), similarly to monoclinic C₂₈H₅₈ n-paraffin studied previously. These and previously obtained data allow us to consider that as the molecular chain length increases, differences in the polymorphic modification of initial crystalline phases cease to be significant and the sequence of polymorphic transformations is mainly determined by the length of the molecule.     

Cohen macaulay rings of global dimension two and krull dimension two

Abstract

We construct an example of an IA-automorphism of the free metabelian group of rank n ≥ 3 without nontrivial fixed points. That gives a negative answer to the question raised by Shpilrain in [Shpilrain, V. (1998). Fixed points of endomorphisms of a free metabelian group. Math. Proc. Cambridge Philos. Soc. 123(1): 75–83. MR 98k:20056]. By a result of Bachmuth [Bachmuth, S. (1965). Automorphisms of free metabelian groups. Trans. Am. Math. Soc. 118:93–1104. MR 31 #4831], such an automorphism does not exist if the rank is equal to 2.     

Derived tame local and two-point algebras

We determine derived representation type of complete finitely generated local and two-point algebras over an algebraically closed field.