The generalized Flanders’ theorem in unit-regular rings
نویسندگان
چکیده
Let R be a unit-regular ring, and let a, b, c ? satisfy aba = aca. If ac or ba is Drazin invertible, we prove that their inverses are similar. Furthermore, if group then similar to ba. For any n?n complex matrices A, B,C with ABA ACA, AC BA only k-powers have the same rank. These generalize known Flanders? theorem proved by Hartwig.
منابع مشابه
A generalized Macaulay theorem and generalized face rings
We prove that the f -vector of members in a certain class of meet semi-lattices satisfies Macaulay inequalities 0 ≤ ∂k(fk) ≤ fk−1 for all k ≥ 0. We construct a large family of meet semi-lattices belonging to this class, which includes all posets of multicomplexes, as well as meet semi-lattices with the ”diamond property”, discussed by Wegner [11], as special cases. Specializing the proof to the...
متن کاملCommuting $pi$-regular rings
R is called commuting regular ring (resp. semigroup) if for each x,y $in$ R there exists a $in$ R such that xy = yxayx. In this paper, we introduce the concept of commuting $pi$-regular rings (resp. semigroups) and study various properties of them.
متن کاملThe unit sum number of Baer rings
In this paper we prove that each element of any regular Baer ring is a sum of two units if no factor ring of R is isomorphic to Z_2 and we characterize regular Baer rings with unit sum numbers $omega$ and $infty$. Then as an application, we discuss the unit sum number of some classes of group rings.
متن کاملGENERALIZED REGULAR FUZZY MATRICES
In this paper, the concept of k-regular fuzzy matrix as a general- ization of regular matrix is introduced and some basic properties of a k-regular fuzzy matrix are derived. This leads to the characterization of a matrix for which the regularity index and the index are identical. Further the relation between regular, k-regular and regularity of powers of fuzzy matrices are dis- cussed.
متن کاملGeneralized f-clean rings
In this paper, we introduce the new notion of n-f-clean rings as a generalization of f-clean rings. Next, we investigate some properties of such rings. We prove that $M_n(R)$ is n-f-clean for any n-f-clean ring R. We also, get a condition under which the denitions of n-cleanness and n-f-cleanness are equivalent.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Filomat
سال: 2022
ISSN: ['2406-0933', '0354-5180']
DOI: https://doi.org/10.2298/fil2208807l