Topic
Idempotence
About: Idempotence is a research topic. Over the lifetime, 1860 publications have been published within this topic receiving 19976 citations. The topic is also known as: idempotent.
Papers published on a yearly basis
Papers
More filters
TL;DR: In this article, the authors define a ring R to be weakly clean if each element of R can be written as either the sum or difference of a unit and an idempotent.
Abstract: Let R be a commutative ring with identity. Nicholson defined R to be clean if each element of R is the sum of a unit and an idempotent. In this paper we study two related classes of rings. We define a ring R to be weakly clean if each element of R can be written as either the sum or difference of a unit and an idempotent and following McGovern we say that R is almost clean if each element of R is the sum of a nonzero-divisor and an idempotent.
71 citations
TL;DR: It is proved that any such discrete idempotent uninorm is uniquely determined by a decreasing function from the set of scale elements not greater than the neutral element to the set on a finite ordinal scale, and vice versa.
Abstract: In this paper we characterize all idempotent uninorms defined on a finite ordinal scale. It is proved that any such discrete idempotent uninorm is uniquely determined by a decreasing function from the set of scale elements not greater than the neutral element to the set of scale elements not smaller than the neutral element, and vice versa. Based on this one-to-one correspondence, the total number of discrete idempotent uninorms on a finite ordinal scale of n + 1 elements is equal to 2n.
70 citations
Posted Content•
TL;DR: This article showed that the walled Brauer algebra is Morita equivalent to an idempotent truncation of a certain infinite dimensional version of Khovanov's arc algebra, as suggested by recent work of Cox and De Visscher.
Abstract: We introduce some graded versions of the walled Brauer algebra, working over a field of characteristic zero. This allows us to prove that the walled Brauer algebra is Morita equivalent to an idempotent truncation of a certain infinite dimensional version of Khovanov's arc algebra, as suggested by recent work of Cox and De Visscher. We deduce that the walled Brauer algebra is Koszul whenever its defining parameter is non-zero.
68 citations
TL;DR: The uninorm-like operations for which the underlying operations are basic pseudo-t-norms and pseudo- t-conorms and one of them is idempotent are described.
68 citations
64 citations