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1.
V. V. Chermnykh 《Journal of Mathematical Sciences》2008,154(2):256-262
The aim of this paper is to study the conditions on the subsemimodule A
S
of the semimodule Γ(P) of all global sections of a sheaf P implying A
S
= Γ(P). Some applications of the developed construction are shown: namely, the Lambek representations for semimodules over strongly
harmonic and reduced Rickart semirings as well as Pierce representations for semimodules over arbitrary semirings were proved
to be isomorphic.
__________
Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 13, No. 2, pp. 195–204, 2007. 相似文献
2.
3.
S. N. Il’in 《Siberian Mathematical Journal》2017,58(2):215-226
We study the semirings whose simple semimodules are all projective. In particular, we establish that for every semiring S this condition implies the injectivity of all simple S-semimodules and show that, in contrast to the case of rings, the projectivity of all simple semimodules in general is not a left-right symmetric property. 相似文献
4.
Two linear maps are usually needed to separate disjoint convex subsets of an idempotent semimodule. In the context of Max-Plus convexity separation can be achieved by a single map if one considers linear maps with values in a linearly ordered semimodule, whose construction is given here, which is not the Max-Plus semiring R∪{-∞}. 相似文献
5.
S. N. Il’in 《Mathematical Notes》2008,83(3-4):492-499
Problems concerning the extension of the Baer criterion for injectivity and embedding theorem of an arbitrary module over a ring into an injective module to the case of semirings are treated. It is proved that a semiring S satisfies the Baer criterion and every S-semimodule can be embedded in an injective semimodule if and only if S is a ring. 相似文献
6.
Yefim Katsov 《Algebra Universalis》2004,51(2-3):287-299
The following analog of the characterization of flat modules has been obtained
for the variety of semimodules over a semiring R: A semimodule
RA is flat (i.e., the tensor
product functor – A preserves all finite limits) iff
A is L-flat (i.e., A
is a filtered colimit of finitely generated free semimodules). We also give new (homological) characterizations of
Boolean algebras and complete Boolean algebras within the classes of distributive lattices
and Boolean algebras, respectively, which solve two problems left open in [14]. It is also
shown that, in contrast with the case of modules over rings, in general for semimodules over
semirings the notions of flatness and mono-.atness (i.e., the tensor product functor – A
preserves monomorphisms) are different. 相似文献
7.
S. N. Il’in 《Russian Mathematics (Iz VUZ)》2013,57(3):26-31
It is well-known that for modules over rings the Baer injectivity criterion takes place. In this paper we prove that under one additional condition this criterion is also valid for modules over semirings. We prove that a semiring S satisfies the Baer criterion if and only if all injective (with respect to one-sided ideals of S) semimodules satisfy the above condition. We propose a newmethod for constructing semirings satisfying the Baer criterion. 相似文献
8.
S. N. Il'in 《代数通讯》2013,41(9):4021-4032
9.
Properties of the idempotently convex hull of a two-point set in a free semimodule over the idempotent semiring R max min and in a free semimodule over a linearly ordered idempotent semifield are studied. Construction algorithms for this hull are proposed. 相似文献
10.
A Characterization of Semirings Which Are Subdirect Products of a Distributive Lattice and a Ring 总被引:9,自引:0,他引:9
S. Ghosh 《Semigroup Forum》1999,59(1):106-120
E -inversive semiring and a Clifford semiring and show that a semiring S is a subdirect product of a distributive lattice and a ring if and only if S is an E-inversive strong distributive lattice of halfrings. Further a Clifford semiring which is, in fact, an inversive subdirect product of a distributive lattice and a ring, is characterized as a strong distributive lattice of rings. Finally, as a consequence of these results we extend a result of Galbiati and Veronesi [2] in the case of Boolean semirings. 相似文献
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13.
Semirings of Formal Power Series 总被引:1,自引:0,他引:1
Semirings of formal power series over semirings, in particular, over k-semifields, are studied. It is also shown that the semiring of formal power series S[[x]] over a k-semifield S becomes a local semiring. Moreover, the Jacobson radical of S[x]] over a k-semifield S is described.AMS Subject Classification (1991): Primary 16Y60 相似文献
14.
This paper continues recent work on N-summations (see [8, 9, 12]). More specifically, it addresses the issue of existence of N-summations both for cone semirings and for prenormed semitopological semimodules. In the case of a cone semiring C we assume N-order completeness plus compatibility of N-joins with addition and multiplication to make the class of summarily bounded elements of C
N
into an N-summation for C. In the case of a prenormed semitopological semimodule M we use certain completeness properties of semitopologies on M to make the class of Cauchy elements of M
N
into an N-summation for M. Results on semitopologies and their connection with closure operators are contained in the Appendix. 相似文献
15.
We relate the old and new cohomology monoids of an arbitrary monoid M with coefficients in semimodules over M, introduced in the author’s previous papers, to monoid and group extensions. More precisely, the old and new second cohomology monoids describe Schreier extensions of semimodules by monoids, and the new third cohomology monoid is related to a certain group extension problem. 相似文献
16.
Jacob C. E. Dekker 《Mathematical Logic Quarterly》1993,39(1):67-78
In transfinite arithmetic 2n is defined as the cardinality of the family of all subsets of some set v with cardinality n. However, in the arithmetic of recursive equivalence types (RETs) 2N is defined as the RET of the family of all finite subsets of some set v of nonnegative integers with RET N. Suppose v is a nonempty set. S is a class over v, if S consists of finite subsets of v and has v as its union. Such a class is an intersecting class (IC) over v, if every two members of S have a nonempty intersection. An IC over v is called a maximal IC (MIC), if it is not properly included in any IC over v. It is known and readily proved that every MIC over a finite set v of cardinality n ≥ 1 has cardinality 2n-1. In order to generalize this result we introduce the notion of an ω-MIC over v. This is an effective analogue ot the notion of an MIC over v such that a class over a finite set v is an ω-MIC iff it is an MIC. We then prove that every ω-MIC over an isolated set v of RET N ≥ 1 has RET 2N-1. This is a generalization, for while there only are χ0 finite sets, there are ? isolated sets, where c denotes the cardinality of the continuum, namely all the finite sets and the c immune sets. MSC: 03D50. 相似文献
17.
Yefim Katsov 《Algebra Universalis》2005,52(2-3):197-214
Among other results on homological characterization of semirings, we prove that the classes of projective and free right (left) semimodules over the polynomial semiring R[x1, x2,..., xn] over an additively regular division semiring R coincide iff R is a field. Also it is shown that an additively regular commutative semiring R is perfect (in H. Basss sense) iff R is a perfect ring.In Celebration of the Sixtieth Birthday of Ralph N. McKenzieReceived July 27, 2003; accepted in final form April 2, 2004. 相似文献
18.
A semiring S whose additive reduct is a semilattice is called a k-regular semiring if for every a∈S there is x∈S such that a+axa=axa. For a semigroup F, the power semiring P(F) is a k-regular semiring if and only if F is a regular semigroup. An element e∈S is a k-idempotent if e+e
2=e
2. Basic properties of k-regular semirings whose k-idempotents are commutative have been studied. 相似文献
19.
S. N. Il’in 《Siberian Mathematical Journal》2012,53(2):222-231
We investigate the semirings over which all simple semimodules are injective. In ring and module theory, the rings with an
analogous condition are called V-rings. Therefore it is natural to call the semirings under consideration V-semirings. We obtain the semiring analogs of some well-known results on V-rings, including an analog of Kaplansky’s theorem on commutative V-rings. 相似文献