Results 61 to 70 of about 708,128 (192)

Bi-artinian noetherian rings [PDF]

Glasgow Mathematical Journal, 2001
A noetherian ring R satisfies the descending chain condition on two-sided ideals (“is bi-artinian”) if and only if, for each prime P ∈ spec(R), R/P has a unique minimal ideal (necessarily idempotent and left-right essential in R/P). The analogous statement for merely right noetherian rings is false, although our proof does not use the full ...
openaire   +2 more sources

Whitehead groups of exchange rings with primitive factors artinian

International Journal of Mathematics and Mathematical Sciences, 2001
We show that if R is an exchange ring with primitive factors artinian then K1(R)≅U(R)/V(R), where U(R) is the group of units of R and V(R) is the subgroup generated by {(1+ab)(1+ba)−1|a,b∈R   with   1+ab∈U(R)}.
Huanyin Chen, Fu-an Li
doaj   +1 more source

Modules over group rings of groups with restrictions on the system of all proper subgroups [PDF]

International Journal of Group Theory, 2015
We consider the class M of R{modules where R is an associative ring. Let A be a module over a group ring RG, G be a group and let L(G) be the set of all proper subgroups of G. We suppose that if H 2 L(G) then A=CA(H) belongs to M. We study an RG{module A
Olga Dashkova
doaj  

On completely 0-simple semigroups

International Journal of Mathematics and Mathematical Sciences, 1996
Let S be a completely 0-simple semigroup and F be an algebraically closed field. Then for each 0-minimal right ideal M of S, M=B∪C∪{0}, where B is a right group and C is a zero semigroup.
Yue-Chan Phoebe Ho
doaj   +1 more source

On Some Classes of Artinian Rings

Journal of Algebra, 2000
The authors study certain classes of Artinian rings whose modules have nice decomposition properties. It is shown that if every countably generated right \(R\)-module is the direct sum of a projective module and a CS-module (i.e., a module with all complements being direct summands), then \(R\) is right Artinian with Jacobson radical cube zero.
Huynh, Dinh Van, Rizvi, S.Tariq
openaire   +1 more source

Continuous rings with ACC on essentials are Artinian

, 1990
It is proved that a left continuous ring with ascending chain condition on essential left ideals is left artinian.
S. Tariq Rizvi, S. R. López-Permouth, S. K. Jain   +2 more
core   +1 more source

DECOMPOSITION OF ARTINIAN ALTERNATIVE RINGS

Mathematics of the USSR-Sbornik, 1982
In der Arbeit werden Zerlegungssätze für artinsche alternative Ringe bewiesen, die für den assoziativen Fall auf \textit{F. Szász} [Bull. Acad. Polon. Sci., Ser. Sci. Math. Astron. Phys. 11, 351--354 (1963; Zbl 0121.04003)], \textit{Dinh Van Huynh} [Math. Nachr. 91, 117--126 (1979; Zbl 0428.16017)], \textit{A. Kertész} und den Autor [J.
openaire   +4 more sources

ARTINIAN \(\mathbf{M}\)-COMPLETE, \(\mathbf{M}\)-REDUCED, AND MINIMALLY \(\mathbf{M}\)-COMPLETE ASSOCIATIVE RINGS

Ural Mathematical Journal
In 1996, the first author defined analogs of the concepts of complete (divisible), reduced, and periodic abelian groups, well-known in the theory of abelian groups, for arbitrary varieties of algebras. In 2021, the first author proposed a modification of
Leonid M. Martynov, Tatiana V. Pavlova
doaj   +1 more source

Differentially trivial and rigid right semi-artinian rings

, 2004
We obtain a characterization of right semi-artinian rings which have only trivial derivations and prove that a rigid (i.e. has only the trivial ring endomorphisms) right semi-artinian ring R is a field or isomorphic to some Zpn
Artemovych, O.D.
core   +1 more source

FCP投射模与某些环(FCP-projective modules and some rings)

Zhejiang Daxue xuebao. Lixue ban, 2010
Let R be a ring. A module MR is called FCP-projective if for every finitely corelated right R-module A. A ring R is called right co-coherent if every finitely cogenerated factor module of a finitely cogenerated injective right R-module is finitely ...
ZHUZhan-min(朱占敏), CHENJian-long(陈建龙)   +1 more
doaj   +1 more source