There are more than 300 different definitions of the sentence, but not a universal one

Adv. Modifier. Trad-ly is a secondary part of the sentence which modifies a predicate-verb, a verbal in any of its function or a part of the sentence expressed by an adjective or adverb.
Semantically can be classified:

• 
  adv. Modifier of time and frequency
  
• 
  adv.modifier of place and direction
  
• 
  adv. Modifier of purpose
  
• 
  adv. Modifier of manner
  
• 
  adv. Modifier of attending circumstances
  
• 
  adv. Modifier of comparison
  
• 
  adv. Modifier of cause
  
• 
  of result
  
• 
  of condition
  
• 
  of concession
  
• 
  of degree and measure
  

Sometimes no clear -cut border-line between a prepositional obj. & adv.modifier( he was looking at the door)
иванова > it is a prepositional Obj, if the use of the prep is governed by the verb. If the use of the prep is optional, Then it’s an adv. Modifier
ильиш suggests the term “neutralization “calls them secondary sentence parts without further subdivision.
Attribute. Trad-ly they serve to modify nouns & noun-equivalents. Structurally are indicated by their position in the sentence. They can be either in pre-position or post-position to the words they modify. Semantically may express various shades of relations with their head nouns. They may be qualitative ( fine days, A ninepenny stamp) circumstantial (a man in love, The key to the door)
Problems:

1. 
   Whether the attr. Is the same synt.level as other secondary sent-members or whether an attr. Is of lower rank, than an obj& the adv.mod
   

Problems of sentence-members:

1. 
   Whether the sec.sent.members are optional . this approach is based on theory of valiancy (валентности). According to this theory –optional and obligatory valiancy are distinguished.
   

The obligatory one is as must, necessarily been realized to complete the sentence structurally. In this connection sec.sent.parts are obligatory, if they form the obligatory valiancy of the pred.
The optional one is such as it isn’t necessarily realized in grammatically complete constructions.( She wrote me a letter- a direct obj. is marked by the obligatory valiancy –of a lower level than apredicate)