منابع مشابه
Non-commutative reduction rings
Reduction relations are means to express congruences on rings. In the special case of congruences induced by ideals in commutative polynomial rings, the powerful tool of Gröbner bases can be characterized by properties of reduction relations associated with ideal bases. Hence, reduction rings can be seen as rings with reduction relations associated to subsets of the ring such that every finitel...
متن کاملOn quasi-zero divisor graphs of non-commutative rings
Let $R$ be an associative ring with identity. A ring $R$ is called reversible if $ab=0$, then $ba=0$ for $a,bin R$. The quasi-zero-divisor graph of $R$, denoted by $Gamma^*(R)$ is an undirected graph with all nonzero zero-divisors of $R$ as vertex set and two distinct vertices $x$ and $y$ are adjacent if and only if there exists $0neq rin R setminus (mathrm{ann}(x) cup mathrm{ann}(y))$ such tha...
متن کاملLWE from Non-commutative Group Rings
The Ring Learning-With-Errors (LWE) problem, whose security is based on hard ideal lattice problems, has proven to be a promising primitive with diverse applications in cryptography. There are however recent discoveries of faster algorithms for the principal ideal SVP problem, and attempts to generalize the attack to non-principal ideals. In this work, we study the LWE problem on group rings, a...
متن کاملON COMMUTATIVE GELFAND RINGS
A ring is called a Gelfand ring (pm ring ) if each prime ideal is contained in a unique maximal ideal. For a Gelfand ring R with Jacobson radical zero, we show that the following are equivalent: (1) R is Artinian; (2) R is Noetherian; (3) R has a finite Goldie dimension; (4) Every maximal ideal is generated by an idempotent; (5) Max (R) is finite. We also give the following resu1ts:an ideal...
متن کاملOn Commutative Reduced Baer Rings
It is shown that a commutative reduced ring R is a Baer ring if and only if it is a CS-ring; if and only if every dense subset of Spec (R) containing Max (R) is an extremally disconnected space; if and only if every non-zero ideal of R is essential in a principal ideal generated by an idempotent.
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ژورنال
عنوان ژورنال: Journal of Algebra
سال: 2001
ISSN: 0021-8693
DOI: 10.1006/jabr.2000.8530