A Counter-example in Jacobson Radicals
نویسنده
چکیده
A plausible conjecture states that an element of the Jacobson radical of the endomorphism ring of an abelian p-group increases the height of any non-zero element of the socle. I construct a counter-example.
منابع مشابه
Hereditary right Jacobson radicals of type-1(e) and 2(e) for right near-rings
Near-rings considered are right near-rings. In this paper two more radicals, the right Jacobson radicals of type-1(e) and 2(e), are introduced for near-rings. It is shown that they are Kurosh-Amitsur radicals (KAradicals) in the class of all near-rings and are ideal-hereditary radicals in the class of all zero-symmetric near-rings. Different kinds of examples are also presented.
متن کاملIntroducing New Structures for D-Type Latch and Flip-Flop in Quantum-Dot Cellular Automata Technology and its Use in Phase-Frequency Detector, Frequency Divider and Counter Circuits
Quantum-dot cellular automata (QCA) technology is an alternative to overcoming the constraints of CMOS technology. In this paper, a new structure for D-type latch is presented in QCA technology with set and reset terminals. The proposed structure, despite having the set and reset terminals, has only 35 quantum cells, a delay equal to half a cycle of clocks and an occupied area of 39204 nm2. T...
متن کاملImproved Constrained PID Control Design based on Connvex-Concave Optimization
In this paper, an algorithm is proposed to improve the design of constrained PID controller based on convex-concave optimization. This design method is based on the optimization of a performance cost function, taking into account the stability and efficiency constraints with frequency domain analysis in which the concepts of sensitivity and complementary sensitivity has been used. It is shown, ...
متن کاملOn group automata over finite fields
We investigate the structure of incidence rings of group automata over finite fields. One of the major tools used in research on the structure of ring constructions is the Jacobson radical. Our main theorem gives a complete description of the Jacobson radicals of incidence rings of (possibly nondeterministic) group automata over finite fields in the important special case where the input group ...
متن کامل$n$-Array Jacobson graphs
We generalize the notion of Jacobson graphs into $n$-array columns called $n$-array Jacobson graphs and determine their connectivities and diameters. Also, we will study forbidden structures of these graphs and determine when an $n$-array Jacobson graph is planar, outer planar, projective, perfect or domination perfect.
متن کامل