Add to ORKGLet R be a ring with center Z, Jacobson radical J, and set N of all nilpotent elements. Call R generalized periodic-like if for all x ∈ R \ (N ∪ J ∪Z) there exist positive integers m, n of opposite parity for which xm − xn ∈N ∩Z. We identify some basic properties of such rings and prove some results on commutativity. Copyright © 2007 H. E. Bell and A. Yaqub. This is an open access article distributed un-der the Creative Commons Attribution License, which permits unrestricted use, distri-bution, and reproduction in any medium, provided the original work is properly cited. 1
Abstract. It is proved that a ring is periodic if and only if, for any elements x and y, there exist...
Abstract. It is proved that a ring is periodic if and only if, for any elements x and y, there exist...
It is proved that a ring is periodic if and only if, for any elements x and y, there exist positive ...
Let R be a ring with center Z, Jacobson radical J, and set N of all nilpotent elements. Call R gener...
Let R denote a ring with center Z, and let N be the set of nilpotent elements. We consider rings def...
Abstract. A well-known theorem of Jacobson (1964, page 217) asserts that a ring R with the property ...
Abstract. A well-known theorem of Jacobson (1964, page 217) asserts that a ring R with the property ...
Abstract. A ring R is called periodic if, for every x in R, there exist distinct positive integers m...
Abstract. We prove that a generalized periodic, as well as a generalized Boolean, ring is either com...
Abstract. We prove that a generalized periodic, as well as a generalized Boolean, ring is either com...
A well-known theorem of Jacobson (1964, page 217) asserts that a ring R with the property that, for ...
A ring is called semi-weakly periodic if each element which is not in the center or the Jacobson rad...
A ring is called semi-weakly periodic if each element which is not in the center or the Jacobson rad...
A ring is called semi-weakly periodic if each element which is not in the center or the Jacobson rad...
Abstract. It is proved that a ring is periodic if and only if, for any elements x and y, there exist...
Abstract. It is proved that a ring is periodic if and only if, for any elements x and y, there exist...
Abstract. It is proved that a ring is periodic if and only if, for any elements x and y, there exist...
It is proved that a ring is periodic if and only if, for any elements x and y, there exist positive ...
Let R be a ring with center Z, Jacobson radical J, and set N of all nilpotent elements. Call R gener...
Let R denote a ring with center Z, and let N be the set of nilpotent elements. We consider rings def...
Abstract. A well-known theorem of Jacobson (1964, page 217) asserts that a ring R with the property ...
Abstract. A well-known theorem of Jacobson (1964, page 217) asserts that a ring R with the property ...
Abstract. A ring R is called periodic if, for every x in R, there exist distinct positive integers m...
Abstract. We prove that a generalized periodic, as well as a generalized Boolean, ring is either com...
Abstract. We prove that a generalized periodic, as well as a generalized Boolean, ring is either com...
A well-known theorem of Jacobson (1964, page 217) asserts that a ring R with the property that, for ...
A ring is called semi-weakly periodic if each element which is not in the center or the Jacobson rad...
A ring is called semi-weakly periodic if each element which is not in the center or the Jacobson rad...
A ring is called semi-weakly periodic if each element which is not in the center or the Jacobson rad...
Abstract. It is proved that a ring is periodic if and only if, for any elements x and y, there exist...
Abstract. It is proved that a ring is periodic if and only if, for any elements x and y, there exist...
Abstract. It is proved that a ring is periodic if and only if, for any elements x and y, there exist...
It is proved that a ring is periodic if and only if, for any elements x and y, there exist positive ...