共查询到20条相似文献,搜索用时 0 毫秒
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Semigroup Forum - For any commutative semigroup S and positive integer m the power function $$f: S \rightarrow S$$ defined by $$f(x) = x^m$$ is an endomorphism of S. We partly solve the... 相似文献
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Acta Mathematica Hungarica - 相似文献
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Tom Head 《Semigroup Forum》1971,2(1):130-137
Let S be a commutative semigroup. S has a greatest regular image if and only if each of its Archimedean components contains
an idempotent. S has a greatest group-with-zero image if and only if S has precisely two Archimedean components and the upper
component contains an idempotent. The existence and structure of these images and of greatest group images is related to tensor
products. 相似文献
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Gary Brookfield 《Semigroup Forum》2003,66(2):323-327
We provide a short proof that a commutative semigroup is finitely generated if its lattice of congruences is Noetherian. 相似文献
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A result of Nakayama and Skornyakov states that a ring R is an Artinian serial ring if and only if every R-module is serial. This motivated us to study commutative rings for which every proper ideal is serial. In this paper, we determine completely the structure of commutative rings R of which every proper ideal is serial. It is shown that every proper ideal of R is serial, if and only if, either R is a serial ring, or R is a local ring with maximal ideal \({\mathcal {M}}\) such that there exist a uniserial module U and a semisimple module T with \({\mathcal {M}}=U\oplus T\). Moreover, in the latter case, every proper ideal of R is isomorphic to \(U^{\prime }\oplus T^{\prime }\), for some \(U^{\prime }\leq U\) and \(T^{\prime }\leq T\). Furthermore, it is shown that every proper ideal of a commutative Noetherian ring R is serial, if and only if, either R is a finite direct product of discrete valuation domains and local Artinian principal ideal rings, or R is a local ring with maximal ideal \({\mathcal {M}}\) containing a set of elements {w 1,…,w n } such that \({\mathcal {M}}=\bigoplus _{i=1}^{n} Rw_{i}\) with at most one non-simple summand. Moreover, another equivalent condition states that: there exists an integer n ≥ 1 such that every proper ideal of R is a direct sum of at most n uniserial R-modules. Finally, we discuss some examples to illustrate our results. 相似文献
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Carmela Musella 《Archiv der Mathematik》2001,76(3):161-165
A group G is said to be a modular group if it has modular subgroup lattice. We will prove in this paper that a polycyclic group G is modular if and only if all its finite homomorphic images are modular groups. Similar results will also be obtained for other conditions of modular type. 相似文献
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Alexander Hulpke. 《Mathematics of Computation》2000,69(232):1633-1651
The lifting of results from factor groups to the full group is a standard technique for solvable groups. This paper shows how to utilize this approach in the case of non-solvable normal subgroups to compute the conjugacy classes of a finite group.
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Commutative monoids all of whose principal ideals are projective 总被引:5,自引:0,他引:5
Mati Kilp 《Semigroup Forum》1973,6(1):334-339
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Semih Koray 《Semigroup Forum》1984,30(1):103-115
Bisimple locally compact topological inverse semigroups whose maximal subgroups are compact and whose set of idempotents is a real interval are studied in this paper. The structure of such semigroups is shown to be entirely determined by their maximal subgroups in case the semigroups come from a certain subclass which includes the connected ones. The factor semigroups moduloH are completely determined. 相似文献
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Jiryo Komeda 《Archiv der Mathematik》2007,89(1):52-59
We consider three subsets of the set of 2n-semigroups, where for a positive integer n a 2n-semigroup means a numerical semigroup whose minimum positive integer is 2n. These three subsets are obtained by the Weierstrass semigroups of total ramification points on a cyclic covering of the
projective line, the Weierstrass semigroups of ramification points on a double covering of a non-singular curve and the Weierstrass
semigroups of points on a non-singular curve. We show that the three subsets are different for n ≧ 3.
Partially supported by Grant-in-Aid for Scientific Research (17540046), Japan Society for the Promotion of Science.
Received: 19 June 2006 相似文献
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根据真理想情况给出了偏序半群的一种分类,研究了真理想为Archimedean子半群的偏序半群的特征. 相似文献
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