منابع مشابه
On the commuting graph of non-commutative rings of order $p^nq$
Let $R$ be a non-commutative ring with unity. The commuting graph of $R$ denoted by $Gamma(R)$, is a graph with vertex set $RZ(R)$ and two vertices $a$ and $b$ are adjacent iff $ab=ba$. In this paper, we consider the commuting graph of non-commutative rings of order pq and $p^2q$ with Z(R) = 0 and non-commutative rings with unity of order $p^3q$. It is proved that $C_R(a)$ is a commutative ring...
متن کاملNon-Commutative First-Order Sequent Calculus
This paper investigates a non-commutative first-order sequent calculus NCLK. For that, this paper extends a non-commutative positive fragment to a full first-order sequent calculus LK− having antecedent-grouping and no right exchange rule. This paper shows (1) NCLK is equivalent to LJ, (2) NCLK with the exchange rule is equivalent to LK, (3) LK− is equivalent to LJ, and (4) translations between...
متن کاملSome Constructions of Non-Commutative Latin Squares of Order n
Let n be an integer. We show the existence of at least three non-isomorphic non-commutative Latin squares of order n which are embeddable in groups when n ≥ 5 is odd. By using a similar construction for the case when n ≥ 4 is even, we show that certain non-commutative Latin squares of order n are not embeddable in groups. Keywords—group, Latin square, embedding.
متن کاملDirected prime graph of non-commutative ring
Prime graph of a ring R is a graph whose vertex set is the whole set R any any two elements $x$ and $y$ of $R$ are adjacent in the graph if and only if $xRy = 0$ or $yRx = 0$. Prime graph of a ring is denoted by $PG(R)$. Directed prime graphs for non-commutative rings and connectivity in the graph are studied in the present paper. The diameter and girth of this graph are also studied in the pa...
متن کاملNon - commutative finite monoids of a given order n ≥ 4
For a given integer n = p1 1 p α2 2 . . . p αk k , (k ≥ 2), we give here a class of finitely presented finite monoids of order n. Indeed the monoids Mon(π), where π = 〈a1, a2, . . . , ak|a p αi i i = ai, (i = 1, 2, . . . , k), aiai+1 = ai, (i = 1, 2, . . . , k − 1)〉. As a result of this study we are able to classify a wide family of the kgenerated p-monoids (finite monoids of order a power of a...
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: Journal of Algebra and Its Applications
سال: 2016
ISSN: 0219-4988,1793-6829
DOI: 10.1142/s0219498817501274