排序方式: 共有35条查询结果,搜索用时 328 毫秒
11.
While a module is pseudo-injective if and only if it is automorphism-invariant, it was not known whether automorphism-invariant modules are tight. It is shown that weakly automorphism-invariant modules are precisely essentially tight. We give various examples of weakly automorphism-invariant and essentially tight modules and study their properties. Some particular results: (1) R is a semiprime right and left Goldie ring if and only if every right (left) ideal is weakly injective if and only if every right (left) ideal is weakly automorphism invariant; (2) R is a CEP-ring if and only if R is right artinian and every indecomposable projective right R-module is uniform and essentially R-tight. 相似文献
12.
François Couchot 《代数通讯》2013,41(10):3418-3423
It is proved that localizations of injective R-modules of finite Goldie dimension are injective if R is an arithmetical ring satisfying the following condition: for every maximal ideal P, R P is either coherent or not semicoherent. If, in addition, each finitely generated R-module has finite Goldie dimension, then localizations of finitely injective R-modules are finitely injective too. Moreover, if R is a Prüfer domain of finite character, localizations of injective R-modules are injective. 相似文献
13.
Let A be a semprime, right noetherian ring equipped with an automorphism α, and let B: = A[[y; α]] denote the corresponding skew power series ring (which is also semiprime and right noetherian). We prove that the Goldie ranks of A and B are equal. We also record applications to induced ideals. 相似文献
14.
Laura Iglésias Catarina Santa-Clara Fernando C. Silva 《Linear and Multilinear Algebra》2013,61(6):651-669
There exist striking analogies in the behaviour of eigenvalues of Hermitian compact operators, singular values of compact operators and invariant factors of homomorphisms of modules over principal ideal domains, namely diagonalization theorems, interlacing inequalities and Courant–Fischer type formulae. Carlson and Sá [D. Carlson and E.M. Sá, Generalized minimax and interlacing inequalities, Linear Multilinear Algebra 15 (1984) pp. 77–103.] introduced an abstract structure, the s-space, where they proved unified versions of these theorems in the finite-dimensional case. We show that this unification can be done using modular lattices with Goldie dimension, which have a natural structure of s-space in the finite-dimensional case, and extend the unification to the countable-dimensional case. 相似文献
15.
K. I. Sonin 《Mathematical Notes》1996,60(2):222-226
16.
Jaime Castro Pérez Mauricio Medina Bárcenas José Ríos Montes Angel Zaldívar Corichi 《代数通讯》2013,41(11):4749-4768
In this article, we investigate some properties of right core inverses. Particularly, new characterizations and expressions for right core inverses are given, using projections and {1, 3}-inverses. Also, we introduced and investigated a new generalized right core inverse which is called right pseudo core inverse. Then, we provide the relation schema of (one-sided) core inverses, (one-sided) pseudo core inverses, and EP elements. 相似文献
17.
Tsiu-Kwen Lee 《代数通讯》2013,41(9):4089-4103
Let R be a ring and ρ a right ideal of R with zero right annihilate. Then ρ and R have the same left Utumi quotient ring. We study the lifting properties of GPIs and some chain conditions inherited by such right ideals. Next, we prove a generalization of Chatters’ theorem. Precisely, we show that if R is a right nonsingular ring with finite right Goldie dimension and possesses a right ideal ρ such that both ρ and l R(ρ) are PI-rings, then the right Utumi quotient ring of R is also a Pi-ring. 相似文献
18.
Jerzy Matczuk 《代数通讯》2013,41(3):725-746
Let a monoid S act on a ring R by injective endomorphisms and A(R; S) denote the S-Cohn–Jordan extension of R. A series of results relating properties of R and that of A(R; S) are presented. In particular it is shown that: (1) A(R; S) is semiprime (prime) iff R is semiprime (prime), provided R is left Noetherian; (2) if R is a semiprime left Goldie ring, then so is A(R; S), Q(A(R; S)) = A(Q(R); S) and udim R = udim A; (3) A(R; S) is semisimple iff R is semisimple, provided R is left Artinian. Some applications to the skew semigroup ring R#S are given. 相似文献
19.
Let R be an associative ring with identity. A unital right R-module M is called “strongly finite dimensional” if Sup{G.dim (M/N) | N ≤ M} < +∞, where G.dim denotes the Goldie dimension of a module. Properties of strongly finite dimensional modules are explored. It is also proved that: (1) If R is left F-injective and semilocal, then R is left finite dimensional. (2) R is right artinian if and only if R is right strongly finite dimensional and right semiartinian. Some known results are obtained as corollaries. 相似文献
20.
In this article we show, among others, that if R is a prime ring which is not a domain, then R is right nonsingular, right max-min CS with uniform right ideal if and only if R is left nonsingular, left max-min CS with uniform left ideal. The above result gives, in particular, Huynh et al. (2000) Theorem for prime rings of finite uniform dimension. 相似文献